Download - Aoptics-instruments

Chapter C apteOptical InstrumentsOptical Instruments

Dr. G. Mirjalili, Physics Dept. Yazd University

General RemarksGeneral Remarks

• Analysis generally involves the laws of reflection and refractionof reflection and refraction

• Analysis uses the procedures of geometrical opticsTo explain certain phenomena the• To explain certain phenomena, the wave nature of light must be usedg


• The Camera


25 1 The Camera25.1 The Camera

• The single-lens h t hi iphotographic camera is

an optical instrument • Components

– Light-tight box– Converging lens

• Produces a real image

– Film behind the lens• Receives the image


Photography lensesg p y

Photography lenses are complex! Especially zoom lensesPhotography lenses are complex! Especially zoom lenses.

Double Gauss Petzval

These are older designsDr. G. Mirjalili, Physics Dept. Yazd University

These are older designs.

PhotographyPhotography lenses

Modern lenses can have up to 20 pelements!

Canon 17-85mm f/3.5-4.5 zoom

Canon EF 600mm f/4L IS USM Super Telephoto Lens17 elements in 13 groups17 elements in 13 groups$12,000


f-number of lens

D U' fnumberf

f

Df

=number-f

The f-number describes the cone angle of the rays that form an image. f f i f i

f

• The brightness of the image• The depth of field• The resolution of the lens

The f-number of a lens determines four important parameters

The resolution of the lens• A lens with a low f-number is a “fast” lens• Simple cameras usually have a fixed focal length and a fixed aperture size, with an ƒ-

number of about 11 (large depth of field)


F-numberThe F-number, “f / #”, of a lens is the ratio of its focal length and its diameter.

numberdiameter.

f ff f

fd1 fd2d2

Fast

f / # = 1 f / # = 2Fast

Dr. G. Mirjalili, Physics Dept. Yazd Universitysmall f-number lenses collect more light but are harder to engineer.

Numeric ApertureThe numeric aperture (N.A.) is the product of the index of refraction (in image space) with the sine of the half-angle of the cone of illumination

Un ′′= sinN.A.

U'D U

f

The f-number of a lens, f/#, is the ratio of the focal length, f, of a lens system to the diameter d of its entrance pupil F/# is inversely proportional to twice the


the diameter, d, of its entrance pupil. F/# is inversely proportional to twice the Numerical Aperture, NA

Optical devices: CameraOptical devices: CameraMultiMulti--element lenselement lens

AS=Iris DiaphragmAS=Iris Diaphragm Film: edges Film: edges

Dr. G. Mirjalili, Physics Dept. Yazd Universityconstitute field stopconstitute field stop

CameraCameraMost common camera is the soMost common camera is the so calledcalled 3535 mmmmMost common camera is the soMost common camera is the so--called called 35 35 mm mm camera ( refers to the film size)camera ( refers to the film size)

27 27 mmmm

34 34 mmmm

Multi element lens usually has a focal length of Multi element lens usually has a focal length of ff ==50 50 mmmm


CameraCamera

Object s = Object s = 1 1 m Image s’ ≈ m Image s’ ≈ 55..25 25 cmcm

Object s = Object s = ∞∞ Image s’ = Image s’ = 55..0 0 cmcm

Thus to focus object between s = Thus to focus object between s = 1 1 m and infinity, m and infinity, jj y,y,we only have to we only have to movemove the lens about the lens about 00..25 25 cm = cm = 22..55mmmm

For most cameras, this is about the limit and it is For most cameras, this is about the limit and it is difficult to focus on objects with s < difficult to focus on objects with s < 1 1 mm


Camera: Brightness of imageCamera: Brightness of imageBrightness of image is determined by the amount of Brightness of image is determined by the amount of light falling on the filmlight falling on the filmlight falling on the film.light falling on the film.

Each point on the film subtends a solid angleEach point on the film subtends a solid angle

22 DDdA DD2

2

2

2

2 4'4 fD

sD

rdAd ππ

===Ω D’D’DD

I di t i tI di t i tIrradiance at any pointIrradiance at any pointon film is proportional on film is proportional to (D/f)to (D/f)22

s’ ≈ s’ ≈ ff

to (D/f)to (D/f)A

Df

= f-number

Dr. G. Mirjalili, Physics Dept. Yazd University2

1A

I p

f number of a lensf-number of a lens

#FDfA ==Define fDefine f--number, number, D,,

This is a measure of the speed of the lensThis is a measure of the speed of the lens 1ISmall f#Small f# (big aperture) I large , t short(big aperture) I large , t shortLarge f#Large f# (small aperture) I small, t long(small aperture) I small, t long

2AI p

fLarge f#Large f# (small aperture) I small, t long(small aperture) I small, t long

fd2

F# 1 F# 1 2Dr. G. Mirjalili, Physics Dept. Yazd University

F# =1 F# =1.2

Standard settings on camera lensesStandard settings on camera lensesStandard settings on camera lensesStandard settings on camera lenses

f# = f/D (f#)2

1 2 1 51.2 1.51.8 3.22 8 7 82.8 7.84.0 165 6 31 55.6 31.58 6411 12116 25622 484

Good lenses, f# = Good lenses, f# = 11..2 2 or or 11..8 8 (very fast) Difficult to get f/(very fast) Difficult to get f/11


Aperture - F #Aperture F #

• F# = f/d• Amount of light proportional to 1/(F#)2• Usual Description

– , , 1.2, 1.8, 2.8, 4, 5.6, 8, 11, 16, ,• Fractional F Stop


Total exposure on FilmTotal exposure on Film

⎞⎛

light

2 )(exposuretimetm

wattsIE •⎟⎠⎞

⎜⎝⎛= film

2mJ

=exposure

Exposure time is varied by the shutter which has settings,1/1000 1/500 1/250 1/100 1/501/1000, 1/500, 1/250, 1/100, 1/50Again in steps of factor of 2


Photo imaging with a camera lens

In ordinary 35 mm camera, the image is very smallIn ordinary 35 mm camera, the image is very small

(i.e. reduced many times compared with the objectAlso, the lens is limited in the distance it can move relative to the film

γ2 large, h2 small

Telephoto and wide angle lens are used in camera

Wide-angle system

γ2 g , 2

systemn1h1γ1= n2h2γ2

γ2 small, h2 large

Telephoto system


Wide angle and Telephoto imagesWide angle and Telephoto images


Telephoto lensLL11 LL22

dd 50 50 mmmmddA larger image can be achieved with a A larger image can be achieved with a telephoto lenstelephoto lensChoose back focal length (bfl ≈ Choose back focal length (bfl ≈ 50 50 mm)mm)Th l b i h d ( i d i )Th l b i h d ( i d i )Then lenses can be interchanged (easier to design)Then lenses can be interchanged (easier to design)The idea is to increase the effective focal length (andThe idea is to increase the effective focal length (andhence image distance) of the camera lens.hence image distance) of the camera lens.


g )g )

Example (telephoto)Example (telephoto)A h h f l h 50 f l l h d h d• Assume that the front lens has +50 mm focal length and the second lens -25 mm focal length. The distance between both is 30mm determine.

• (a) the focal length.• (b) the actual physical length of the system.

f1=+50mm f2=-25mm

30mmfilm


30mm

SolutionSolution

for this telephoto lens the focal length is:for this telephoto lens the focal length is:

mmffF 250)25)(50(21 +=−+

== mmdff

F 25030255021

+=−−+

=−+

=

H2

film

250 mm2

Th f l l th f th t i th di t f thThe focal length of the system is the distance from the second principal plane, H2 of the system to the filme in the camera.


SolutionSolution

• Physical length of the system1 PPP += P1=1/(+50)x10 -2)=+20

2

1

2

)(1P

ndP

P +−

= P1=1/(+50)x10 )=+20

P2=1/(-25X10 -2) =- 40

20+P

11

10)40()03.0)(20(1

202 =−+

+−+

=

mmmP

a 1001.01011

2

2 ====

The physical length is:

30+100 = 130 mm = 13 cm

It is acceptable.


Depth of FieldOnly one plane is imaged (i.e., is in focus) at a time. But we’d like objects near this plane to at least be almost in focus. The range of

It depends on how much of the lens is used, that is, the aperture.

j p gdistances in acceptable focus is called the depth of field.

p p

Out-of-focusObject

f

Out of focus plane

Object

Image

Size of blur in out-of-focus

planef

Focal planeAperture

Dr. G. Mirjalili, Physics Dept. Yazd UniversityThe smaller the aperture, the more the depth of field.

Depth of fieldDepth of field

The range of distances in acceptable focus is called the depth of field.

DbD D

∆ffff

fb

ffD

⟨⟨∆∆

=∆+

bDfb

fD

ff

∆=

⟨⟨∆

f ∆f

D

fbf

ff

=∆

∆


f ∆fDf∆

Depth of field example A large depth of fieldp p A large depth of field isn’t always desirable.

f/32 (very small aperture; large depth of field)large depth of field)

f/5 (relatively large aperture; small depth of field)small depth of field)

A small depth of field is also desirable for portraits.


p

Depth of FieldIf d is small enough (e.g. less than grain size of film emulsion ~ If d is small enough (e.g. less than grain size of film emulsion ~ 1 1 µm)µm)then the image of these points ill be acceptablethen the image of these points ill be acceptable

ss22 ss22’’then the image of these points will be acceptablethen the image of these points will be acceptable

ss11 ss11’’

dd

xx xx

ss ss ’’Dr. G. Mirjalili, Physics Dept. Yazd University

ssoo ssoo’’

Depth of Field (DOF)

ds 'S`1=S`0+X

A f/D

Ddsx o=

A=f/D

( )o Adffss += 21 ddαα αα

DD( )o

o

Adffss

Adsf−

=

+

2

21

xx xxoAdsfs

−22

ss ’’Dr. G. Mirjalili, Physics Dept. Yazd University

ssoo’’

Depth of fieldDepth of field

2224

2

12)(2 oo

dAfffsAdsssDOF −

=−= 222412osdAf −

e.g. d = e.g. d = 1 1 µm, f# = A = µm, f# = A = 44, f = , f = 5 5 cm, scm, soo = = 6 6 mm

DOF = DOF = 00..114 114 mm

i.e. si.e. soo = = 6 6 ±± 00. . 06 06 mm


Depth of fieldDepth of fieldStrongly dependent on the f# of the lensStrongly dependent on the f# of the lens

( )Adff 00010+

g yg ySuppose, sSuppose, soo = = 44m, m, ff = = 5 5 cm, d = cm, d = 40 40 µmµm

1200

( )AAdsf

Adffsso

o

6.125000,10

21 +≈

++

= 1000

sDOF = s2 – s1 600

800 s2

D th f fi ld (f )(cm

)

400

s

Depth of field (focus)

s 1,s2 (

( )AAdsf

Adffsso

o

6.125000,10

22 −≈

−−

=0

200s1

Dr. G. Mirjalili, Physics Dept. Yazd University0 2 4 6 8 10 12 14 16

0

f#

ApertureAperture

• Other effects and usage of aperturesapertures


Aperture have an image in the optical system

E l

Aperture have an image in the optical system

• Example

i=14

F=9cm

E t

Exit pupil

Entrance pupil

• A stop 8 mm in diameter is placed halfway between• A stop 8 mm in diameter is placed halfway between image and lens. What is the diameter and where is the place of the exit pupil?.


SolutionSolution

cmif

ifo 2.25149

)9)(14(−=

−=

−=

cmo 6.122

2.25−=

−=′ Place of entrance pupil

cmfo

foi 6.319)6.12()9)(6.12(

2

=+−

−=

+′′

=′ Place of Exit pupilfo 9)6.12( ++

oi

DD

EP

XP

′′

=

cmo

iDD EPXP

EP

26.12

)5.31)(8.0(=

−=

′′

= Diameter of Exit pupil


Do the exit pupil and entrance pupil lie on the same side?

Yes!If the stop is moved even closer

fIf the stop is moved even closerTo the lens (with in the focal length)The exit pupil is virtual p pand lie on the entrance side

Entrance pupil

Exit pupil


Aperture of combination of lensesAperture of combination of lensesp=+8Th t il i th

P=?.

p +8The entrance pupil is the image of the aperture formed by the first lens

8cm

fThe exit pupil is the image of the aperture formed by the second lensthe second lens

Example:Example:in the Fig. the power of the minus lens is unknown. The system is afocal, The

apertue diameter is 15 mm and is placed half way between the lenses.

(a)- where is the entrance pupil?

(b) -where is the exit pupil ?

Dr. G. Mirjalili, Physics Dept. Yazd University(c) -What are their diameters?

Solution

• The focal length of the first lens is:• (1/8)(100)=12.5cm• The second lens must have:

(12 5 8)= 4 5 cm-(12.5-8)=- 4.5 cmThe entrance pupil is the image of the aperture formed by first lens;

of )512)(4( − cmfo

ofi 88.5)5.12()4()5.12)(4(

2

2 +=+

=+

= To the right of the first lens

The exit pupil is the image of the aperture formed by second lens

cmi 12.2)54()4(

)5.4)(4(−=

−+−−−

=′ To the left of second lens)5.4()4( +


Solution (cont )Solution (cont,)

Th h l Whi h i i l f f lThey are a the same place. Which is typical of an afocal system

The intrance pupil size:

mmiD

D aperture 22)8.58)(15(==

′= mm

oDEP 22

40==

′=

The exit puple size

mmDxp 840

)2.21)(15(==


SummeryThe effects of aperture (stop Diaphragm) inThe effects of aperture (stop, Diaphragm) in

the optical system

• 1- control of the entrance and the exit pupils

• 2- effect on the depth of field2 effect on the depth of field• 3-reduces the aberrations


The Eyey


The EyeThe Eye

• The normal eye focuses light and produces a sharplight and produces a sharp image

• Essential parts of the eye– Cornea – light passes

through this transparent structurestructure

– Aqueous Humor – clear liquid behind the corneaq


The cornea, iris, and lens-The cornea is a thin membrane that has an index of refraction of around 1.38.

-The cornea the eye and refracts light (more than the lens does!) as it enters the eyethe eye. -Some light leaks through the cornea, especially when it’s blue.

-The iris controls the size of the pupil, an opening that allows light to enter through.

-The lens is jelly-like lens with an index of refraction of about 1.44.

Thi l b d th t th i i b fi t d-This lens bends so that the vision process can be fine tuned.--The ciliary's muscles bend and adjust the lens.


Human Eye, Relaxed20 mm

15 mm

n’ = 1.33

F F’H H’

3.6 mm

Dr. G. Mirjalili, Physics Dept. Yazd University7.2 mm P = 66.7 D

Accommodation

• Refers to changes undergone by lens toRefers to changes undergone by lens to enable imaging of closer objects

• Power of lens must increase• Power of lens must increase• There is a limit to such accommodation

h d bj i id ’ “however and objects inside one’s “near point” cannot be imaged clearly

• Near point of normal eye = 25 cm• Fully accommodated eye P = 70 7 for s =Fully accommodated eye P = 70.7 for s =

25 cm, s’ = 2 cm


HYPERMETROPIA: TYPESHYPERMETROPIA: TYPES

• Axial: Eye short relative to its focal power (ie can have normal length or be ( gpathologically shortened)

• Refractive/Index: Inadequate refractive• Refractive/Index: Inadequate refractive power -> includes aphakia

• Curvature: Curvature of refracting surface too flat eg cornea planatoo flat eg cornea plana


Myopia: Near Sightednessy p g

Eyeball too large ( or power of lens too large)Eyeball too large ( or power of lens too large)


Myopia – Near SightednessFar point of the eye is much less than Far point of the eye is much less than ∞, e.g. ∞, e.g. llff

Must move object closer to eye to obtain a clear imageMust move object closer to eye to obtain a clear imageust o e object c ose to eye to obta a c ea ageust o e object c ose to eye to obta a c ea age

Normal N.P.Normal N.P.

MyopicMyopic MyopicMyopicDr. G. Mirjalili, Physics Dept. Yazd University

y py p

F.P.F.P.

y py p

N.P.N.P.

MyopiaMyopia e.g. le.g. lff = = 22mmgg ff

1'1 H ill thH ill th

fn

l1

''1=+

How will the How will the near point be near point be affected?affected?fsl f ' affected?affected?

00..5 5 + + 6666..7 7 = = 6767..2 2 DDi l d fi l d f t l !t l !P=-0 5 D is relaxed power of eye is relaxed power of eye –– too large!too large!

To move far point to To move far point to ∞, must decrease power to ∞, must decrease power to 6666..77Use negative lens with P =Use negative lens with P = 00 55 DD

P=-0.5 D


Use negative lens with P = Use negative lens with P = --00..55 DD

Laser Eye surgeryLaser Eye surgery

Radial Keratotomy Radial Keratotomy –– Introduce radial cuts to the Introduce radial cuts to the cornea of the elongated, myopic eyeballcornea of the elongated, myopic eyeball

Usually use the Usually use the 1010..6 6 µm line of a COµm line of a CO22 laser for laser for almost almost 100100% % absorption by the corneal tissueabsorption by the corneal tissue BlurredBlurredp yp y BlurredBlurred

visionvision

Dr. G. Mirjalili, Physics Dept. Yazd UniversityFront viewFront view

Laser Eye surgeryy g yRadial Keratotomy Radial Keratotomy –– Introduce radial cuts to the Introduce radial cuts to the ad a e atoto yad a e atoto y t oduce ad a cuts to t et oduce ad a cuts to t ecornea of the elongated, myopic eyeballcornea of the elongated, myopic eyeball

Usually use theUsually use the 1010 66 µm line of a COµm line of a CO22 laser forlaser forUsually use the Usually use the 1010..6 6 µm line of a COµm line of a CO22 laser for laser for almost almost 100100% % absorption by the corneal tissueabsorption by the corneal tissue

DistinctDistinctFlatteningFlattening

Distinct Distinct visionvision

Dr. G. Mirjalili, Physics Dept. Yazd UniversityFront viewFront view

Hyperopia – Far Sightednessyp p g

Eyeball too smallEyeball too small or lens of eye can’t fully accommodateor lens of eye can’t fully accommodateEyeball too small Eyeball too small –– or lens of eye can’t fully accommodateor lens of eye can’t fully accommodate

Image of close objects formed behind retinaImage of close objects formed behind retinag jg j


Hyperopia – Far Sightedness

Suppose near point =Suppose near point = 11mmSuppose near point = Suppose near point = 11mm

n'1 Dsn 7.677.661'1

1=+=+

s1P=+3 D

Recall that for a near point of Recall that for a near point of 25 25 cm, we need cm, we need 7070..77DDUse a positive lens with Use a positive lens with 3 3 D power to correct this person’s D power to correct this person’s vision (e.g. to enable them to readvision (e.g. to enable them to read))

Usually means they can no longer see distant objectsUsually means they can no longer see distant objects -- Need bifocalsNeed bifocalsDr. G. Mirjalili, Physics Dept. Yazd University

Usually means they can no longer see distant objects Usually means they can no longer see distant objects -- Need bifocalsNeed bifocals

Correction lenses for myopia and hyperopiaCorrection lenses for myopia and hyperopia


AstigmatismAstigmatism

Astigmatism due to eye’s lens being elliptical, which causes the focus in the vertical to differ from horizontal.

Vertical focus

Astigmatism may be corrected using a cylindrical lenscylindrical lens.In this example, the lens focuses in the horizontal only since vertical is already in focus.


already in focus.

Astigmatism is a common problem in the eye.


Slenen tableS e e tab ed

D

tagθ = d/D =1.5x10-3/5 =1`

(eye resolution)(eye resolution)



Diff f l l h f i li dDifferent focal length for inclined rays


ASTIGMATISM: TYPESASTIGMATISM: TYPES

1 R l P i i l idi t 90• 1. Regular: Principal meridians at 90degrees to each other and at/near 90 & 180 degrees. (WTR & ATR)

• 2. Oblique: Principal meridians at 90q pdegrees to each other but NOT at/near 90 & 180 degrees.& 80 deg ees

• 3. Irregular: Principal meridians NOT at 90 degrees to each other90 degrees to each other.


ASTIGMATISM: TYPES (Regular)ASTIGMATISM: TYPES (Regular)

• Regular: Principal meridians at 90 degrees to each other and at/near 90 & g180 degrees. (WTR & ATR)

ATRWTR ATR


ASTIGMATISM: TYPES (oblique)ASTIGMATISM: TYPES (oblique)

• Oblique: Principal meridians at 90 degrees to each other but NOT at/near 90g& 180 degrees.


ASTIGMATISM: TYPES (irregular)ASTIGMATISM: TYPES (irregular)

• 3. Irregular: Principal meridians NOT at 90 degrees to each other.g


0

54

.54

0cylindrical

• .54spherical

55

55

55

spherical 55

52

p

57astigmatism


CLASSIFICATION: REGULAR ASTIG’M

• 1. Simple: One o.t. foci falls on the retina. Can be hypermetropic (other focus behind the retina) or myopic (other focus in front o.t. retina)

• 2. Compound: Neither focus on retina but both either in front or behind it. Can, again, be hypermetropic or myopic

• 3. Mixed: One focus in front & other focus behind the retinabehind the retina


Simple AstigmatismSimple Astigmatism

• . Simple Astigmatism: One of the foci falls on the retina. Can be hypermetropic (other focus behind the retina) or myopic (other focus in front of the retina

Retina 54C

Simple myopic astigmatism 57

Cornea

Retina 51

Simple hypermetropic astigmatism

54


Compound AstigmatismCompound Astigmatism

• 2. Compound: Neither focus on retina but both either in front or behind it. Can, again, , g ,be hypermetropic or myopic

Retina 57

Compound myopic astigmatism

Retina

58g

Retina 51

Compound hypermetropic astigmatism

52


astigmatism

Mixed astigmatismMixed astigmatism

• 3. Mixed: One focus in front & other focus behind the retina

57

5252


REGULAR ASTIGMATISM ILLUSTRATEDREGULAR ASTIGMATISM ILLUSTRATED

• Retina a = compound hypermetropic• Retina b = simple hypermetropic• Retina c = mixedRetina c mixed• Retina d = simple myopic

Retina e = compound myopic• Retina e = compound myopic


.

•The Eye spectacles (eyeglass)( y g )


COMPONENTS OF THE OPHTHALMIC

• The ophthalmic prescription can be broken into three sets of numbers – Sphere

Cylinder– Cylinder– Axis

Sphere-Cylinder-Axis

+2D, +3D,x650


SphereSphere

• The first set of numbers represents the spherical portion of the prescription p p p p

33 0000 22 0000 180180--33..0000--22..0000xx180180(sphere) (cylinder) (axis)


CylinderCylinder

• The second set of numbers represents the amount of astigmatism correction (cylinder g ( y

+3.00--22..0000x180(sphere) (cylinder) (axis)


Cylinder and astigmatism system

• Cylindrical lenses have curvature and• Cylindrical lenses have curvature and refracting power in only one meridian.

• They may be convex or concave. • Cylinders focus light rays to a focal line• Cylinders focus light rays to a focal line.• A spherocylinder is a combination of a

sphere and a cylinder (astigmatism).


AxisAxis

• The third set of numbers represents the proper lens orientation for correcting p p gastigmatism (axis)

++33..0000-2.00x180180( h ) ( li d ) ( i )(sphere) (cylinder) (axis)


AxisAxis

• In cylindrical lenses, the meridian perpendicular to the meridian with p pcurvature is the axis.

1800

450900

1350

18000 Axis=900 18001800

3

33

0Axis=180 0


0

SphericalSpherical

• If it is a spherical only prescription the word sphere or abbreviation sph should be p pused to indicate the prescription is complete without cylindercomplete without cylinder

+3 00 sphsph+3.00 sphsph51 +3 54

+ =51 3

54

54Spectacle


51 +3

CylinderCylinder

• If there is a cylinder component, there must also be an axis noted

+3.00 Cyl X9000

3



• If there is a astigmatism component, there must be an sphere, cylinder and axis p , ynoted

++33 0000 -2 00 x180180++33..00 00 2.00 x180 180 (sphere) (cylinder) (axis)


ExampleExample• What is the following prescription? which kind of

astigmatism is the eye?57 +1 - 4 54 5457

58 0 - 4

= + =

54 54

450

+1 cyl. - 4 sph x45 axis

+1 Cyl., -4 Sph., x45

Oblique astigmatism


PrismPrism

• Prism may be incorporated into eyeglass lenses and in some cases rigid contact glenses to correct diplopia.

• If prism is prescribed the power of prism• If prism is prescribed the power of prism, expressed in diopters as well as the

f ’orientation of the prism’s base must be included.


Prism• ∆ is the symbol for Prism

• BI (BASE IN) (Used to treat Exotropia/phoria)

• BO (BASE OUT) (Used to treat Esotropia/phoria)

• BU (BASE UP) (Used to treat Hypotropia/phoria)

• BD (BASE DOWN) (Used to treat Hypertropia/phoria)


PrismPrism

• +3 00-2 00x180 1 ∆ B I+3.00-2.00x180 1 ∆ B I(1 prism diopter base in)


Add powerAdd power

• Amount of plus power required for near use in addition to the power required for p qdistance.


Add powerAdd power

• +3 00 2 00x180• +3.00-2.00x180 +2.50 add


Transpositions of prescriptionsTranspositions of prescriptions

• Prescriptions containing spherocylindrical l b itt i i li dlenses may be written in minus-cylinder or plus-cylinder form.

• Converting from one form to another is called transpositioncalled transposition.



The mathematic manipulation is as follows:• algebraically add the cylindrical power to• algebraically add the cylindrical power to

the sphere• reverse the sign of the cylinder• add or subtract 90˚ to make the new axisadd or subtract 90 to make the new axis

180˚ or less



+3 00 2 00 180 b +1 00+2 00 090+3.00-2.00x180 becomes +1.00+2.00x090


Other measurements required to make eyeglasses

Interpupillary distance (pd or ipd)• Measurement is very important whenMeasurement is very important when

making eyeglasses It i di t h t l th ti l• It indicates where to place the optical centers in the finished lenses.

• The optical center of a lens denotes the point of optimal visionpoint of optimal vision.



Interpupillary distance (pd or ipd)• (This measurement may be included with(This measurement may be included with

the prescription or the measurement may be taken by the optician making thebe taken by the optician making the glasses.)

pd pd



Vertex distance• This measurement is the distance from theThis measurement is the distance from the

back surface of an eyeglass lens to the front surface of the patient’s corneafront surface of the patient s cornea.

• This measurement becomes an important factor in prescriptions greater than +5.00 or -5.00 diopters.or 5.00 diopters.

eyeglass eyeV.D



Vertex distance • (This measurement may be included with(This measurement may be included with

the prescription or the measurement may be taken by the optician making thebe taken by the optician making the glasses, when applicable. This

fmeasurement is performed using a distometer.))



BBase curve• Lens “blanks” supplied by manufacturers have a single

curve the base curve Starting with this curve the labcurve, the base curve. Starting with this curve the lab technician grinds additional curves on the lens surface to achieve the final power. Patients can become accustomed to wearing a particular• Patients can become accustomed to wearing a particular base curve. If a new pair of glasses is made with a different base curve the patient may experience di f t i f ild t Th hth l idiscomfort, ranging from mild to severe. The ophthalmic technician may be responsible for measuring the base curve of eyeglasses. This is done using a Geneva lens l kclock.


Other information required to dispense contact lenses

Th ifi ti f ti t’ t t l• The specifications for a patient’s contact lenses differs from a prescription for eyeglasses,

• Depending on the office policy regarding the• Depending on the office policy regarding the fitting of contact lenses the following information may be provided to patients for a contact lens yprescription.

• If it is the policy of the office NOT to fit contact lenses a patient may take their eyeglasslenses, a patient may take their eyeglass prescription to an optometrist or ophthalmologist who fits contact lenses to perform a contact lenswho fits contact lenses to perform a contact lens fitting.


•The doctor “fitting” the contactThe doctor fitting the contact lenses is not required to use the patient’s existing eyeglasspatient s existing eyeglass prescription and may require the patient to have a complete exampatient to have a complete exam.• The doctor that prescribes the contact lenses should see the patientcontact lenses should see the patient in follow-up to confirm the fit of the

t t l d kcontact lenses and make modifications as necessary.


Other information required to dispense contact lenses

• spherical equivalent (when applicable)• spherical equivalent (when applicable)• keratometry readings• lens diameter

b• base curve• lens thickness• material of the lens• water content (if soft)• specific brand or type• edge blends or peripheral curves (if any)g p p ( y)• lens tint (if any)• wearing instructions


to



Spectacle PrescriptionSpectacle PrescriptionDr. Laser Wong, B.Sc., M.Sc., PhD.

O P T O M E T R I S T SLaser Centre, Rm CD623, The Hong Kong Polytechnic University, , , g g y y,

Hunghom, Kowloon, Hong Kong (852) 2766 5677SPECTACLE LENS PRESCRIPTION

Name:__________________________ Date:_________________

SPHERE CYLINDER AXIS PRISM BASE ADDRx SPHERE CYLINDER AXIS PRISM BASE ADD

D.V.O.D.

O.S.

N.V.O.D.

O SO.S.

SPECIAL INSTRUCTIONS_____________________________________

Dr. G. Mirjalili, Physics Dept. Yazd UniversityDR_____________________________________

D.V.This part of the prescription describes the corrections for Distant Vision.N.V."Near vision."O.D.O D is an abbreviation for "oculus dexter " Latin for "right eye "O.D. is an abbreviation for oculus dexter, Latin for right eye.O.S.O.S. is an abbreviation for "oculus sinister," Latin for "left eye."

SphereSphereA minus sign denotes near-sightedness or myopia while a plus sign denotes far-sightedness or hyperopia.

CylinderIf there is a value under this heading then you have astigmatismIf there is a value under this heading, then you have astigmatism.

AxisAs mentioned above, a special cylindrical lens is needed in order to correct astigmatism. Not only does the strength of the cylindrical lens need to be specified, but the lens itself must be rotated into a specific position in order to provide the proper vision correction. The axis represents the amount of rotation of the cylindrical lens in degrees ranging from 1 to 180 PrismThis is a box on the prescription form that is rarely filled in. Occasionally, when the two eyes are notThis is a box on the prescription form that is rarely filled in. Occasionally, when the two eyes are not properly aligned and looking directly at the same thing, prism can be ground into the lenses in order to re-align them.

Add

Dr. G. Mirjalili, Physics Dept. Yazd UniversityIf there is a value under the 'add' heading, then you have a bifocal prescription.

• Simple Magnifier


Simple MagnifierSimple Magnifier

• A simple magnifier consists of a single converging lensg g

• This device is used to increase the apparent size of an objectapparent size of an object

• The size of an image formed on the retina depends on the angle subtended by the eyeeye


Simple magnifierSimple magnifierIn order to see something better we need a larger image of it on the In order to see something better, we need a larger image of it on the retina of our eyes. We can see something better--make a larger image on the retina--by bringing it closer to our eyes.

N.P

However, . . .Our eyes are only able to focus a clear, sharp image from an object only so close. That distance is called the near point of your eye. As you move an object closer than the near point, the image

Dr. G. Mirjalili, Physics Dept. Yazd Universityformed on the retina become blurry and fuzzy.

Simple MagnifierSimple Magnifier• A simple magnifier consists of a single converging lens

• This device is used to increase the apparent size of an object

• The size of an image formed on the retina depends on the angle subtended by the eye

• With a single lens, it is possible to achieve angular magnification up to about 4 without serious aberrationsmagnification up to about 4 without serious aberrations

• With one or two additional lenses, which correct the b ti ifi ti f t b t 20 baberrations, a magnification of up to about 20 can be

achieved


The Size of a Magnified ImageThe Size of a Magnified Image• When an object is placed at the near point, the angle subtended is maximum

– The near point is about 25 cm• When the object is placed just inside the focal point of a converging lens, the lens forms a

virtual, upright, and enlarged image


Angular MagnificationAngular MagnificationAngular MagnificationAngular MagnificationA l ifi ti i d fi d• Angular magnification is defined as

cmph

m 25lenswithangle===≡

θpcm

hm25lenswithoutangleo

===≡θ

• The angular magnification is a maximum when the image formed by the lens is at the near point of the eyep ~ f cmCalculated by

m 25cm=

i th h t th f l l th th b tt

fmmax =


i.e. the shorter the focal length the better

• Compound Microscope


Compound Microscope(refractive )Compound Microscope(refractive )

• A compound microscope consistsmicroscope consists of two lenses– Gives greater g

magnification than a single lensTh bj ti l– The objective lens has a short focal length, ƒo<1 cmg , ƒo

– The ocular lens (eyepiece) has a f l l th ƒ f Note: q1≈L andand pp11≈f0

Dr. G. Mirjalili, Physics Dept. Yazd Universityfocal length, ƒe of a few cm

Note: q1≈L and and pp11≈f0

Image plane #2

Image plane #1

Eye-piece

ObjectiveMicro- plane #2

M1 M2

plane #1 pieceMicroscopes

Microscopes work on the same principle as telescopes, except that the object is really close and we wish to magnify it. j y g y

When two lenses are used, it’s called a compound microscope.

Standard distances are s = 250 mm for the eyepiece and s = 160 mmStandard distances are s 250 mm for the eyepiece and s 160 mmfor the objective, where s is the image distance beyond one focal length. In terms of s, the magnification of each lens is given by:

|M| = di / do = (f + s) [1/f – 1/(f+s)] = (f + s) / f – 1 = s / f


MicroscopeMicroscope terminology


Compound Microscope contCompound Microscope, cont.

• The lenses are separated by a distance L– L is much greater than either focal length

• The approach to analyze the image formation is the same as for any two lenses in a row– The image formed by the first lens becomes the

object for the second lens• The image seen by the eye, I2, is virtual, 2

inverted and very much enlarged


Magnifications of the Compound Microscope

• The lateral magnification of the objective is1

1 ƒL

pqM −≈−=

• The angular magnification of the eyepiece of 01 ƒp

the microscope iscm25

ee

cm25ƒ

m =


eƒ

Overall magnificationOverall magnification

• The overall magnification of the microscope is the product of the individual magnificationsg

⎞⎛ cm25L

⎠

⎞⎜⎜⎝

⎛−== e1

cm25ƒƒ

LmMm⎠⎝ eo ƒƒ


Other Considerations with a MicroscopeOther Considerations with a Microscope

Th bilit f ti l i t i bj t• The ability of an optical microscope to view an object depends on the size of the object relative to the wavelength of the light used to observe itg g– For example, you could not observe an atom (d ≈ 0.1

nm) with visible light (λ ≈ 500 nm)


Reflector microscopeReflector microscope

Many creative designs exist for microscope objectives. Example: the Burch reflecting j p gmicroscope objective:

Object To eyepiece


• SOME CAULCULATION about the microscope+matrix is neededp


• Telescopes


• HISTORY OF TELESCOPE


The History of the TelescopeThe History of the Telescope

• It is a common misconception that Galileo invented the first telescopesp

• In fact, Hans Lippershey, a Dutch spectacle make is credited with designingspectacle make, is credited with designing the first telescope

• Galileo is the first person known to have turned a telescope to the skyturned a telescope to the sky


Galileo’s TelescopeGalileo s Telescope

• He was astonished by what he saw– The rings of Saturng– Stars in the Milky Way

The moons of Jupiter– The moons of Jupiter– Spots on the sun

• He also went blind


Telescopes ( t’d)(cont’d)

The Galilean TelescopeThe Galilean Telescope

f1 < 0 f2 > 0

The analysis of this telescope is a homework problem!


Telescopes TodayTelescopes Today

• Telescopes have come a long way since then

• The biggest single telescopes have main mirrors that are over 12 meters inmirrors that are over 12 meters in diameter!

• Some telescopes are actually arrays that are made of dozens of smaller telescopesare made of dozens of smaller telescopes linked together


Three Types of TelescopesThree Types of Telescopes

• Optical– Refracting g– Reflecting

R di• Radio• Spacep


How Telescopes WorkHow Telescopes Work

• There are two main types of optical telescopesp– Refracting telescopes use lenses to focus

light to a pointlight to a point– Reflecting telescopes use mirrors to focus

the lightthe light– Catadioptric telescopes are a combination of

th tthe two


Refracting and Reflecting Telescopes


Anatomy of a TelescopeAnatomy of a Telescope

• Although there are many types of telescopes, all have some basic key parts:p , y p

• The aperture is simply the part of the telescope that lets light intelescope that lets light in

• The primary bends the light, bringing the rays to a point

• The secondary aids in this process• The secondary aids in this process


Focusing LightFocusing Light

• The idea of focusing light is important– Telescopes collect light from a large areap g g– By focusing the light, we concentrate its

powerpower• The focal plane is the plane where the

li ht tlight rays meet• The focal length is the distance from theThe focal length is the distance from the

primary lens (or mirror) to the focal plane


The Focal PlaneThe Focal Plane

• If we put our eye at the focal plane, we would only see a bright pointy g p

• The eye piece straightens out the rays of light so our eye can see the imagelight so our eye can see the image

• If we move the eyepiece out of the focal plane, the image will be distorted


Anatomy of a TelescopeAnatomy of a Telescope

• The optical tube protects the rest of the telescope and blocks stray rays of lightp y y g

• The finder is a small telescope used for honing in on objectshoning in on objects

• The detector is the thing that actually records the light– Could be your eyeCould be your eye


Type of Telescopes : Refractor

Advantage glass surface inside the tube is sealed from the atmosphere

rarely needs cleaning → optical alignment is stable

no air currents and effects of temperature change no air currents and effects of temperature changeimages are steadier and sharper


Refracting TelescopeRefracting Telescope

• The two lenses are arranged so that the objective forms aso that the objective forms areal, inverted image of a distance objectThe image is near the focal• The image is near the focal point of the eyepiece

• The two lenses are separated by the distance ƒo + ƒe, which corresponds to the length of the tube

• The eyepiece forms an enlarged, inverted image of the first image N t θ h’/f d θ h’/f


first image Note: θ≈h’/fe and θ0 ≈h’/f0

Telescope TerminologyTelescope Terminology


Refractor TelescopsRefractor Telescops

Newton

Gregory Cassegrain Schwarzschid


Gregory g

Type of Telescopes : RefractorDisadvantageDisadvantage chromatic aberration

lens focuses differently with wavelength(the shorter the wavelength, the greater the amount of refraction)

li ht i b b d b th l light is absorbed by the lensopaque to UV, IR region

large lens is quite heavythe lens tends to deform under its own weighthard to make large lensthe largest refractor : 1.02m of Yerkes Observatory

difficult to make a glass lens with no imperfections inside the lens and with a perfect curvature on both sides of the lens


lens and with a perfect curvature on both sides of the lens

Type of Telescopes : Refractorchromatic aberration Produces a rainbow of colors around the image Produces a rainbow of colors around the image.

Because of the wave nature of light, the longer wavelength light (redder colors) is bent less than the shorter wavelength light (bluer colors) as it passes through the lens.

This is used in prisms to produce pretty rainbows, but can it ruin an image!


Type of Telescopes : Reflector

Advantage no chromatic aberration can be made very BIG! can be made very BIG! cheaper one side of the telescope's objective needs to be perfect


Reflecting Telescope Newtonian FocusReflecting Telescope, Newtonian Focus

• The incoming rays are reflected from the mirror and converge toward point Aconverge toward point A– At A, a photographic plate

or other detector could be l dplaced

• A small flat mirror, M, reflects the light toward an opening in th id d i tthe side and passes into an eyepiece


Type of Telescopes : ReflectorDisadvantage Tube is open to the outside and optics need frequent cleaning Tube is open to the outside and optics need frequent cleaning

disturbing the optical alignment

Often a secondary mirror is used to redirect the light into a more convenient viewing spot. The secondary mirror and its supports can produce diffraction effects: bright objects have spikes (theproduce diffraction effects: bright objects have spikes (the “christmas star effect”).


Type of Telescopes : Reflector10 meter Keck telescope at the W.M Keck Observatory


Spherical Aberration If the mirror is not curved enough paraboloid or if the glass lens is not shaped correctly.

Not all of the light is focused to the same point

In the case of paraboloid, all parallel rays come to a single focus, which is not the case for a sphere


is not the case for a sphere.

Spherical AberrationExample: Hubble Space Telescope Soon after HST put in orbit (1990), found that could not find good focus of images (circle of least confusion very ugly).

Too flat by 2 microns (1/50 the width of a human hair) Too flat by 2 microns (1/50 the width of a human hair)2.5 years after lunch, install corrective optics (COSTAR)


Spherical Aberration

Before COSTAR After COSTARDr. G. Mirjalili, Physics Dept. Yazd University

Before COSTAR After COSTARDr. G. Mirjalili, Physics Dept. Yazd University

Design of Reflector Telescope(1) Prime Focus small f ratio

d b lk f inconvenient to suspend bulky pieces of equipment

(2) Newtonian(2) Newtonian for small telescope attaching heavy instruments → unbalance the telescope


Type of Telescopes : Reflector(3) Cassegrain

convenient attaching instruments

(4) Coude large heavy instruments (e g spectrograph) large heavy instruments (e.g. spectrograph)

→ need separate room altitude-azimuth mounting

→ Nasmyth platform


Type of Telescopes : Reflector Same telescope (with fixed tube) can be reconfigured to different

focal lengths. ff f ffDifferent focal lengths lead to different “plate scales” (image

sizes) and allows different fields of view or resolution for the same focal plane area.

Can have different instruments mounted at different “ports”.

Traditional reflectors (e.g., Palomar 200", Kitt Peak 4-m) wereoften designed with at least FOUR configurations possible: g g p

- Prime focus: Usually a wide field of view camera. - Cassgrain focus: Spectrograph of higher resolution camera. - Newtonian focus: Spectrograph of higher resolution camera.

Coude focus: VERY high resolution spectrographDr. G. Mirjalili, Physics Dept. Yazd University

- Coude focus: VERY high resolution spectrograph.

Type of Telescopes : Reflector Multiple focus port


Type of Telescopes : Reflector Note the problem of the Prime Focus: It is in the beam of the

telescope and so difficult to access.

Prime focus of the Palomar 200 inch telescopeDr. G. Mirjalili, Physics Dept. Yazd University

Prime focus of the Palomar 200 inch telescope

h•The 3 Main Functions f T lof Telescopes


VignettingVignetting


Marc Pollefeys

The 3 Main Functions of Telescopes1. GATHER LIGHT – make things appear brighter

2. RESOLVE – allow finer detail to be seen

3. MAGNIFY – make objects seem bigger/closerj gg /


Powers of a Telescope : Light-Gathering Power

The ability of a telescope to collect a lot more light than the human eyeeye.

The telescope acts as a “light bucket‘”, collecting all of the photons.a bigger objective collects more light in a given time interval.the pupils of your eyes enlarge at night so that more light reaches

the retinas .

M ki f i t i b i ht i iti l if th li ht i i t b Making faint images brighter is critical if the light is going to be dispersed to make a spectrum.


Powers of a Telescope : Light-Gathering Power

Light gathering power the area of the objectiveFor the circular objectives For the circular objectives

area = π × (diameter of objective)2/4

Example:a 40-centimeter mirror has four times the light-gathering power asa 40 centimeter mirror has four times the light gathering power asa 20-centimeter mirror


Light Gathering Power

The light-gathering power of a telescope is directly proportional to the area of the objective lens, which in turn is proportional to the square of the lens di

Dr. G. Mirjalili, Physics Dept. Yazd Universitydiameter

ResolutionResolutionThe ability of an optical• The ability of an optical system to distinguish between closely spaced y pobjects is limited due to the wave nature of lightConsider two not• Consider two not coherent light sources (like stars) ( )

• Because of diffraction, the images consist of bright central regionsbright central regions flanked by weaker bright and dark rings (a) Images are resolved and (b) not

resolved (sources too close)Dr. G. Mirjalili, Physics Dept. Yazd University

gresolved (sources too close)

Rayleigh’s CriterionRayleigh s Criterion

If th t t d th t th i• If the two sources are separated so that their central maxima do not overlap, their images are said to be resolvedsaid to be resolved

• The limiting condition for resolution is Rayleigh’s CriterionCriterion– When the central maximum of one image falls on the

first minimum of another image, they images are saidfirst minimum of another image, they images are said to be just resolved

– The images are just resolved when their angular separation satisfies Rayleigh’s criterion


Just ResolvedJust Resolvedθmin

• If viewed through a slit of width a and applying Rayleigh’sa, and applying Rayleigh s criterion, the limiting angle of resolution is

aλθ =min

• For the images to be resolved, the angle subtended by the two

a

the angle subtended by the two sources at the slit must greater than θmin


Barely Resolved (Left) and Not Resolved (Right)

Not resolved

Barely resolved


resolvedresolved

Resolution with Circular AperturesResolution with Circular Apertures

• The diffraction pattern of a circular aperture consists of a central, circular bright region surrounded by progressively fainter ringsprogressively fainter rings

• The limiting angle of resolution depends on the diameter, D of the apertureD, of the aperture

λθ 1.22min = For circular patternDmin pattern


Resolving Power of a Diffraction GratingResolving Power of a Diffraction Grating

• If λ1 and λ2 are two nearly equal wavelengths between which the grating spectrometer can just barely distinguish the resolving power R of the grating isdistinguish, the resolving power, R, of the grating is

λλRλλ−λ ∆

==12

R

– All the wavelengths are nearly the same


Resolving Power of a Diffraction Grating, cont

• A grating with a high resolving power can distinguish small differences in wavelengthdifferences in wavelength

• The resolving power increases with order number R = Nm– R = Nm

• N is the number of lines illuminatedm is the order n mber• m is the order number

– All wavelengths are indistinguishable for the zeroth-order maximum mmaximum

• m = 0 so R = 0

m=1

m m


m=0

m=2

Powers of a Telescope : Resolving Power

Ability to make us see really small details and see sharp images. Objects that are so close together in the sky that they blurj g y ytogether into a single blob are easily seen as separate objects with a good telescope.

The resolving power = absolute smallest angle that can be resolved

ΘR (arcsec) = 252,000 × (λ/D)

where λ : observation wavelengthgD : objective diameter


Powers of a Telescope : Resolving Power ΘR (arcsec) = 252,000 × (λ/D)

Th d i i t k ll ibl The desire is to make as small as possible.

This can be done by making the observation wavelength small (e.g., use UV instead of visible light) or by making the objective diameter large.

Example: ΘR of the 40-cm telescope is one-half the for the 20-cm telescope

Fluctuations in the atmosphere

i ffseeing effect



Large size of radio telescopeRadio wavelengths are LARGE so the radio telescope must beRadio wavelengths are LARGE so the radio telescope must be LARGE to get decent resolving power

Example : Keck 10m telescope vs. 305m Arecibo Radio telescope



Example:

1 Å = 0.1 nm = 10-10 m

6000 Å ~ 10-7 m = 10-5 cm for visible wavelength6000 Å ~ 10 m = 10 cm for visible wavelength

21 cm for radio wavelength = visibleRF

DDλλ

wavelength diffrence ~ 106 7

11021

=−

− opticaltescopRadio

D

DD

1m optical telescope 666 1010210211

≈×=×=−

−

telescopRadio

telescopradio

DD

Need 106m (103km) radio telescope with comparable resolvingpower of 1m optical telescope !


Infrared spectroscopyInfrared spectroscopy

• .



Another way to increase the resolution is to connect telescopes together to make an interferometer.g

large single telescope !



EXAMPLES of Interferometer Very Large Array (VLA)y g y ( )

- This telescope is made of 27 radio dishes, each 25 meters in diameter, on a Y-shaped track.

F ll t d d th V L A i 36 kil t d- Fully extended, the Very Large Array is 36 kilometers across and has a resolution of around one arc second (depending on the radio wavelength).



EXAMPLES of Interferometer Very Long Baseline Array (VLBA)y g y ( )

- a huge interferometer that uses ten telescopes placed in sites from Hawaii to the Virgin Islands

8 600 kil t d h l ti d 0 0002- 8,600 kilometers across and has a resolution as good as 0.0002 arc second!

- With a resolution about 50 times better than the Hubble Space pTelescope



The Orbiting Very Long Baseline Interferometer (OVLBI)- Astronomers are constructing radio telescopes out in space that g p p

will work in conjunction with ground-based radio telescopes to make interferometers much larger than the Earth.



Another EXAMPLES of interferometer in optical telescope

the Keck Interferometer on Mauna Kea, Hawaii

the Very Large Telescope of Paranal Observatory on Cerro Paranal in the Atacama Desert, northern Chile.



All have the same brightness

- The light in the bottom images from the large telescopes is just much moretelescopes is just much more Concentrated than for the small telescopes.

- Exposure time with large telescope is short !


Poor and Great Resolution (i d b i d i i )(improved by using adaptive optics)

Telescope images are degraded by the blurring effects of the atmosphere and

Dr. G. Mirjalili, Physics Dept. Yazd Universityby light pollution

Powers of a Telescope : Magnifying Power

The ability of a telescope to enlarge images

Th l t i t t f t l b it l The least important power of a telescope because it enlarges any distortions due to the telescope and atmosphere.

A small fuzzy faint blob becomes only a big fuzzy blobA small, fuzzy faint blob becomes only a big, fuzzy blob. the light becomes more spread out under higher magnification sothe image appears fainter!

Magnifying power = (focal length of objective) / (focal length of eyepiece)( g j ) / ( g y p )

fE

T

ffM=


light pollutionTelescope images are degraded by the blurringTelescope images are degraded by the blurringeffects of the atmosphere and by light pollution

• Angular Resolution: A telescope’s angular resolution, whichAngular Resolution: A telescope s angular resolution, which indicates ability to see fine details, is limited by two key factors

• Diffraction is an intrinsic property of light waves• Its effects can be minimized by using a larger objective lens or• Its effects can be minimized by using a larger objective lens or

mirror• The blurring effects of atmospheric turbulence can be minimized by

l i th t l t t ll t i ith th iplacing the telescope a top a tall mountain with very smooth air.• They can be dramatically reduced by the use of adaptive optics and

can be eliminated entirely by placing the telescope in orbit


Electromagnetic Spectrum for Telescope


Electromagnetic (EM) Spectrum for TelescopeTHOUGHT PROBLEM TIME OUT:1.What parts of the EM spectrum can astronomers explore from sea

level ?level ?

2. What parts of the EM spectrum can astronomers explore from2. What parts of the EM spectrum can astronomers explore from high mountain tops?

3 Wh f l ibl i h h i i f3. What types of astronomy were only possible with the invention of high altitude balloons and rockets?

4. Why is there concern about “ozone holes” for people living near the poles of the Earth? (Note: UV radiation is blocked primarily by absorption of ozone molecules in the Earth's atmosphere )absorption of ozone molecules in the Earth s atmosphere.)


Electromagnetic (EM) Spectrum for Telescope

The Earth's atmosphere is opaque to most wavelengths in the electromagnetic spectrum. This is good for lifeforms on Earth's surface because the more energetic This is good for lifeforms on Earth s surface, because the more energetic

types of EM radiation are harmful. But obviously, this is not convenient for astronomers who want to

monitor the universe across the full EM spectrum (This is the mainmonitor the universe across the full EM spectrum. (This is the main motivation for space astronomy.)

Th h b h h bili f diff l hDr. G. Mirjalili, Physics Dept. Yazd University

The chart above shows the ability of different wavelengths to penetrate the atmosphere.

Atmospheric TransparencyAtmospheric Transparency


Electromagnetic (EM) Spectrum for TelescopeSome places on the surface of the Earth are not high and dry

enough so airborne observatories are often used for infrared astronomyastronomy.

NASA's Stratospheric Observatory for Infrared Astronomy (SOFIA) is a 2.5-m telescope in a modified Boeing 747 and should begin flying in a few years.


g g y g y



A radio telescope uses a large concave dish to reflect radio waves to a focus

• Radio telescopes use large reflecting antennas or dishes to focus radio waves

• Very large dishes provide reasonably sharp radio images


Radio TelescopesRadio Telescopes

• Large antenna that receive parts of the spectrum other than visible light.


Hubble Space TelescopeHubble Space Telescope

• Launched from the Space Shuttle

• Had problems that were later fixed while in space.

• Able to see muchAble to see much further than earth bound telescopesbound telescopes



DetectorsDetectors

• So, we collected all our light…now what?• It doesn’t do us any good if we can’t seeIt doesn t do us any good if we can t see

the lightOf l h• Of course, we always have our eyes, but…


Photographic PlatesPhotographic Plates

• When the photograph was invented, it revolutionized astronomyy

• You could expose of long periods of time and have a permanent recordand have a permanent record


MagnificationMagnification

• Astronomer’s do like magnification, too– But note that it does not matter how much you y

magnify something…if you cannot resolve it, magnification does you no goodg y g

– Think of a pixelated image


PixelationPixelation


Photographic PlatesPhotographic Plates

• But photographic plates have lots of shortcomingsg

• They over expose easilyTh h li• They have a non-linear response

• You cannot actually count photonsou ca ot actua y cou t p oto s• They are not very efficient


CCDsCCDs

• CCDs revolutionized astronomy again• CCD stands for charged coupled deviceCCD stands for charged coupled device• This is the same technology at use in

di it ldigital cameras


How CCDs work


Most digital cameras interleave different-color filters


CCDsCCDs


CCDsCCDs


CCDsCCDs

• CCDs are great because– They are very efficienty y– They allow you to take digital data…analyze

on computeron computer– They have a linear response

Th h id d i– They have a wide dynamic range


CCDsCCDs

• CCDs are by far the most common detector in astronomyy

• Although some others exist, it is not worth talking about them heretalking about them here


SpectrographsSpectrographs

• We don’t always want to make an image• Sometimes we want to split the light intoSometimes, we want to split the light into

its spectrumW t h f thi• We use spectrographs for this


SpectrographsSpectrographs

• There are two basic types of spectrographsp g p– Prisms

Gratings– Gratings• Combining the two, we get Grisms


PrismsPrisms

• Prisms work because light of different wavelengths takes a slightly different pathg g y p

• Comes out at a different place, and is thus spread outspread out


Spectrographs record the spectra of astronomical objects.


Spectrographs record the spectra of astronomical objects.


Observations at other wavelengths are revealing previously invisible sightsrevealing previously invisible sights.

UV infraredUV infrared

O diMap of

Ordinary visible

pOrion region


GratingsGratings

• Gratings are made up of hundreds or thousands of tiny groovesy g

• They use a phenomenon of light known as diffraction to split the lightdiffraction to split the light


GrismsGrisms

• Grisms use both effects

• Gratings and grisms are the most commonly used spectrographs in astronomy

Dr. G. Mirjalili, Physics Dept. Yazd University Dr. G. Mirjalili, Physics Dept. Yazd University

Telescopes Image plane #1

Image plane #2Telescopes

M1 M2

plane #1 plane #2

Keplerian telescope

A telescope should image an object, but, because the object will have a very small solid angle, it should also increase its solid angle

telescope

y g , gsignificantly, so it looks bigger. So we’d like D to be large. And use two lenses to square the effect.

01/ 1/imaging

MO

f M⎡ ⎤

= ⎢ ⎥−⎣ ⎦where M = - di / do1/ 1/f M⎣ ⎦

2 10 01/ 1/ 1/ 1/telescope

M MO

f M f M⎡ ⎤ ⎡ ⎤

= ⎢ ⎥ ⎢ ⎥⎣ ⎦ ⎣ ⎦

Note that this is easy for the first lens, as the object

2 2 1 11/ 1/ 1/ 1/telescope f M f M⎢ ⎥ ⎢ ⎥− −⎣ ⎦ ⎣ ⎦1 2 0M M⎡ ⎤

= ⎢ ⎥So use di << do

is really far away!

Dr. G. Mirjalili, Physics Dept. Yazd University1 2 2 1 1 2/ / 1/M f M f M M= ⎢ ⎥− −⎣ ⎦

i ofor both lenses.

• Lensometer


Lensometry Lensometry


LensometerLensometer

– .


What is Lensometry?What is Lensometry?

Lensometry is the procedure used to measure the prescription of a patient’smeasure the prescription of a patient s existing eyeglass lenses or the power of

t t l Alth h lcontact lenses. Although some people refer to this as neutralization, this is technically incorrect. The term neutralization applies to retinoscopy.pp py


Lensometry measures four principal properties of lenses:

• Spherical and cylindrical power p y pin dioptersA i if li d i l• Axis, if cylindrical

• Prism amount and direction if• Prism, amount and direction, if any

• Optical centers


How is Lensometry performed?How is Lensometry performed?

Lensometry is performed with a specialized instrument know as a lensometer.

Manual Manual LensometerLensometer

Automated Automated LensometerLensometer


LensometerLensometer

Types of LensometersTypes of Lensometers• Lensometers may be either manual or automatedLensometers may be either manual or automated.

There are several manufacturers for each. • To perform manual lensometry the operator should• To perform manual lensometry, the operator should

have a thorough understanding of lensometry as well as optical principleswell as optical principles.

• Performing automated lensometry requires very littl kill k l d f tilittle skill or knowledge of optics.

• Automated lensometry may be quicker to perform but in most cases the instrument is more expensive to purchase than a manual lensometer.


Performing Manual LensometryPerforming Manual Lensometry

Although most manual lensometers look similar despite a different brand name, the p ,buttons and knobs may be placed differently on certain models and the miresdifferently on certain models and the mires may have a slightly different appearance. The technique is the same for plus andThe technique is the same for plus and minus cylinder.


The following principles may be applied to all manual lensometers:

The first three steps in performing lensometry on lenses of all types are:

1. Focusing the instrument eyepiece2. Positioning the eyeglass lens to be measured2. Positioning the eyeglass lens to be measured

on the specific table (or frame support platform) of the lensometerof the lensometer

3. Measuring the sphere power and, if present cylinder power and axis either plus or minuscylinder power and axis, either plus or minus cylinder form.


EyepieceEyepiece


Focusing the EyepieceFocusing the EyepieceY t f th i i t• You must focus the eyepiece prior to using the lensometer, failure to do so could result in erroneous readings

• With no lens in the lensometer, look ,through the eyepiece of the instrument

• Turn the power wheel until the mires• Turn the power wheel until the mires (the perpendicular crossed lines), viewed through the eyepiece are totallyviewed through the eyepiece, are totally out of focus


Focusing the EyepieceFocusing the Eyepiece

• Turn the eyepiece toward the plus direction• Slowly turn the eyepiece in the oppositeSlowly turn the eyepiece in the opposite

direction until the target is clear• Turn the power wheel to focus the mires• Turn the power wheel to focus the mires• The mires should focus at a reading of zero

(plano)(plano)• If the mires do not focus at plano, repeat

h f h b i ithese steps from the beginning


Positioning the eyeglass lensPositioning the eyeglass lensPower wheel

Platform / table

Gimbal


Power wheel

Axis wheelAxis wheel


Measure the sphere power

Align the lens so that the mires cross in the center of the target (if unable consider prism)


Thin “single” lines that represent the sphereThin, single lines that represent the sphere

Perpindicular, widely spaced thick lines that represent the cylinder


Measuring the sphere powerMeasuring the sphere power

• Turn the power wheel either direction to focus the mires

if all the mires come into focus at the same time…

Record the number on the power wheel, This is a spherical only RxThis is a spherical only Rx


CylinderCylinder

if all the mires do not come into focus at the same time

Si lt l t t th i h l t f d• Simultaneously rotate the axis wheel to focus and straighten the thin sphere lines, record the number on the power wheel this is the sphere poweron the power wheel, this is the sphere power

• Leaving the axis as it is, bring the thick lines into focus by turning the sphere wheelfocus by turning the sphere wheel


Cylinder

• Algebraically add the number shown now on the power wheel with thenow on the power wheel with the number previously recorded as the sphere this is the cylinder amountsphere, this is the cylinder amount, record the axis

• To transpose the cylinder, rotate the axis 90˚and start overa s 90 a d sta t o e


Lensometry technique for multifocal lenses

If the glasses are multifocal the first step is to determine the distance Rx. For a traditional lined segment add you would then reposition the glasses so that the center of the bifocal add is in the lensometer gimbal.


The absolute power of the bifocal segment is always p g ymore plus (or less minus) than the sphere power in the upper (distance) portion of an eyeglass lens. The dd i th t t l diff i di t iadd is the total difference in dioptric power.



Measuring trifocal powerMeasuring trifocal power

To measure the trifocal segment directly, To measure the trifocal segment directly, follow the same procedure as for the bifocalfollow the same procedure as for the bifocalfollow the same procedure as for the bifocal follow the same procedure as for the bifocal segment, reading the distance segment first, segment, reading the distance segment first, the intermediate segment second and thethe intermediate segment second and thethe intermediate segment second, and the the intermediate segment second, and the near segment last. It is standard for the near segment last. It is standard for the trifocal power to betrifocal power to be 5050% of the bifocal power;% of the bifocal power;trifocal power to be trifocal power to be 5050% of the bifocal power; % of the bifocal power; therefore the usual protocol would be not to therefore the usual protocol would be not to measure the power of the trifocalmeasure the power of the trifocalmeasure the power of the trifocal.measure the power of the trifocal.


Progressive add multifocal lensesProgressive add multifocal lenses•Progressive add lenses are different from•Progressive add lenses are different from traditional bifocal or trifocal eyeglasses in that there are no visible segments dividing the distance andare no visible segments dividing the distance and reading portions of the lenses.

• In order to create this “no-line” appearance the manufacturing processes often produce unwanted cylinder power, distortion, or blurred transition zones between the distance and near segments. This can make lensometry a little tricky.


Progressive add multifocal lensesProgressive add multifocal lenses• When performing lensometry on progressive-p g y p g

add eyeglasses try to select the area with the least distortion in both distance and the reading

ti f th l b f t ki diportions of the lenses before taking a reading.

• Because of the nature of the progressive add, p g ,the strongest portion of the add is close to the bottom of the lens, so try to read the add as close to the bottom of the lens as possible.

• Other than these issues lensometry is performed Other than these issues lensometry is performed the same way as with conventional multifocals.


Placement of optical centers• Optimal vision correction is achieved when

pp

looking through the optical center of the eyeglass lens. The lensometer may be

d t if th iti f th ti lused to verify the position of the optical center of a lens.

• Position the frame in the lensometer as if f i b i l t kperforming basic lensometry, make sure

the frame is sitting flat on the platform and is lined up properly Focus the mires andis lined up properly. Focus the mires and center in the target.


Placement of optical centersp

the picture on the left is an example of properly aligned mires and

target, at this point you would dot the lens


Placement of optical centersPlacement of optical centers

• If equipped, use the dotting device on the lensometer to mark the lens. Thisthe lensometer to mark the lens. This mark will be the optical center. If th i d tti d i th• If there is no dotting device, then use a nonpermanent marker to mark the approximate center of the lens.


Placement of optical centersPlacement of optical centers

• Once the optical center of both lenses has been found, a millimeter ruler ishas been found, a millimeter ruler is used to measure the distance between the marks on the lensesthe marks on the lenses.

• This distance should match the patient’s interpupillary distance unless there is prism in the lenses.p s t e e ses


Lensometry technique for prisms

L t t l


• Lensometry measures not only the power of a prism but also thethe power of a prism but also the orientation of the prism base.

• The prism orientation may be base in (toward the nose) basebase in (toward the nose), base out (toward the temple), base up,out (toward the temple), base up, or base down.



If i i d i th l


• If prism is ground in the lens you will not be able to align the mireswill not be able to align the mires with the target.

• As mentioned in the previous chapter regarding optical centerschapter, regarding optical centers, if the pupil measurement is “off”if the pupil measurement is off prism will be induced.


Measuring prism power and orientationMeasuring prism power and orientation

• OK, you can’t line the mires up with the target…so you have prism, right? Now g y p , ghow do you find out how and what type?...

the picture on the left is a representation of mires that cannot

be aligned with the target due to prism (not drawn to scale)


To measure the amount of prismTo measure the amount of prism

• Count the number of circles from the central cross of the target to the center gof the mires (each circle represents 1 prism diopter)prism diopter)

• Record the direction of the base faccording to the displacement of the

mires (example: if mires are displaced ( p pdown, the prism is base down)


Some lensometers are made to Some lensometers are made to compensate for prism If yourcompensate for prism If yourcompensate for prism. If your compensate for prism. If your lensometer has a feature of this type, lensometer has a feature of this type, please refer to the instruction manual please refer to the instruction manual for more information Also somefor more information Also somefor more information. Also some for more information. Also some lensometers have auxiliary prisms in lensometers have auxiliary prisms in the case that there is more prism than the case that there is more prism than there are circles on the target.there are circles on the target.there are circles on the target.there are circles on the target.


THE END

Th k Y !THE END

Thank You!


Dr. G. Mirjalili, Physics Dept. Yazd University Dr. G. Mirjalili, Physics Dept. Yazd University