ECE 5616Curtis

Instruments and the Optical Invariant

• Telescopes• M=1/Mθ• Microscopes and eye pieces• Camera• Fiber Optics• Spectrometers• Optical Disk

• media • laser isolation• optical head• optical system with servo signal

• Optical Invariant

ECE 5616Curtis

Example: The TelescopeKeplerian

Shown in the afocal geometry (d=f1+f2). Relaxed eye focuses at ~1m, thus telescope are usually not afocal. Analysis simpler, however.

Definition of angular magnification

Via similar triangles

This is both important and fundamental.

ECE 5616Curtis

Example: The TelescopeGalilean

yu

h10

h1-h1/f1

h1- h1(f1+f2)/f1-h1/f1 – (h1-h1(f1+f2)/f1)/f2=0

h1- h1(f1+f2))/f1 = -h2-h1/f1 – (h1-h1(f1+f2)/f1)/f2

M = h2/h1 = -f2/f1

() =h1f2/f1 -h2 = h1f2/f1

But f2 is negative so M>0

ECE 5616Curtis

Example: The TelescopeGalilean

Note that formula is identical to Keplerian.This is the advantage of the sign convention.

hh

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Reflective Telescopes

Chromatic aberration is very small with mirrors, transmission can be very high, light weight

Magnification same as Keplerian / Galilean

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Magnifier - through anglesUseful for infinite conjugates

For a equal focal lengths, fe, visual magnification should beproportional to ratio of angles

Via similar triangles

via lens power equation

Dnp=10 inch, shortest distance an eye can focus to

-tm

Dnp

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Compound Microscope

Focus by moving object relative toboth lenses and stop

L-Tube length

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Visual magnification is product of linear mag of objective and mag of eyepiece:

Microscope

Remember M=-xi/F (thin lens)

Standard Near Point is 10 inches (254mm)

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Eye PiecesUsed with microscope and telescopes

HuygensRamsden

Kellner

Can get Zemax examples

If standard NP=10 inches a 10x eye piece would have a F=1 inch

Cheap but bad eye relief Cheap but better eye relief (common)

Achromatic Ramsden, wide field

ECE 5616Curtis

More Eye Pieces

Orthoscopic Plossl (symmetrical)

Erfle Most common wide field EP

Better image qualityBetter image quality over field

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Camera

SLR – Single Lens Reflex Camera

35mm Camera• wide range of F available cheaply• 46.5mm from mount to film plane• Nikon, Canon major vendors• Zeiss, Leica, Tamron, Tokina, Scheider, etc• Image size: 24 mm×36 mm.

Medium and Large Format CameraHasselblad (Zeiss), Mammia56.5 x 56.5mm film sizes plus110mm F2, Hasselblad ~ 5-6kBFL=74.9mm

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Film (Field) sizes

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Wide AngleF= 6mm-40mmFOV 50-220°

Standard

StandardF= 50-65mmFOV 40-50°

1893, Fewest # elements with 3rd ab 0

1840, portrait lens

Camera Lenses

You can find Zemaxexamples online

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Nikon AF Micro-Nikkor105mm f/2.8

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Hasselblad 80mm, f/2.8

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Fiber Optics

−−

−=== cca nnNA θθθ 211 cos1sinsin

Multimode step index

Single mode

Multimode gradient index

22

21

2

1

21 1 nn

nnnNA −=⎟⎟⎠

⎞⎜⎜⎝

⎛−=

What is the NA that the fiber can accept/ send out ? Core is n1 and cladding is n2

Ex: n1=1.475, n2=1.46 then NA=.21 and θa=12 degrees

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IS

m sinsin ±=λα

α is the angle diffractedλ is the wavelength of lightm is the order numberI is the incident angle + sign is for transmission, - is for reflective gratingS – is the period of the grating (spacing of the grating lines)

Spectrometersusing gratings

Grating equation

Since angle depends on λ, can use to measure wavelength

ECE 5616Curtis

Spectrometersusing gratings

The dispersion of the grating is dθ/dλ (differentiating the grating equation)

dθ/dλ = m/(S cosθ)

The effective width of a line is equal to Δα=2π/N, where N is the number of grating lines illuminated (assuming the Aperture Stop is the grating) Δα can be written as (kS/2) (sinθ – sinθi) or (kS/2) cosθ (Δθ).

This can be written asdθmin = 2λ/(NS cosθm)This is the FULL angular width of a line due to instrument broadening

Plug this into above equation and solve for dλ results inλ/dλmin = mN = R( resolving power) = NS(sinα ± sinI)/λ

Or dλmin = λ/mN6in wide grating at 15,000lines/in in 2nd order will resolve180,000 lines, at 540nm dλ = 0.003nm

ECE 5616Curtis

Optical disks• Probably the largest volume optical system ever –

CD,DVD, BD– 10’s of million devices per year

• First video disk in early 1970 – killed (12 inch)• CD mid 1970’s

– First CD-R from Sony cost $15,000– Current OEM price for CDROM is ~8 dollars

– ~10 Billion disks per year• CD price are <20 cents a disk with 10 cents being IP royality• DVD’s maybe 50 cents

– Record and read by focusing beam to diffraction limited spot andchanging reflectivity or polarization state of media

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Focus ServoFx>Fy

A+D-(B+C)Or (AD-BC)

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Tracking Servo

If NA of lens is > 0.5λ/p orders will overlap

Where p is grating period (track width)

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Optical Head Write Once Drive

• MO has polarizer between PBS and toric lens• Data signal is transitions for bright state to dark state. RLL codes are used to make sure timing stays sync’ed

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Laser Feedback Elimination

“Optical recording”, Alan Marchant, Addison Wesley

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Recordable Media

Examples include: InSeTe and GeSeTe and many others flavors

Phase Change: Sole survivor

Magneto-optical materials

Being considered for next gen hard drives

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Optical InvariantAt image/object plane (special case)

Paraxial Snell’s Law

Triangles

Substitute into M

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Optical InvariantAt image/object plane (special case)

Invariant – this expression has the same value everywhere in the optical system.

At an object or image plane the invariant is equal to the index times the object/image height times the half convergence/divergence angle of the axial beam

ECE 5616Curtis

Optical invariantaka Lagrange or Helmholtz invariant

is conserved everywhere

At a general surface anywhere in the optical system the invariant is expressed as

The 3D version for throughput is that the product of the object/image area times the solid angle of collection is invariant

Write the paraxial refraction equations for the marginal ray (PMR)and chief or pupil ray (PPR):

With a bit of algebra:

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Basic Definitions

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Examples• Given object and image slopes and object height

can find height of image.– uo = .333, ui=-0.04755, h=20mm– M=h’/h => h’= (20)(0.333)/(-0.04755)= -14.0187mm

• Image height for lens with object at infinity– Y for axial ray is 0, slope of u is zero, up is half FOV

INV = h’n’u’ = -y1nup

h’ = -upy1/u’ for n=n’F= -y1/u’ soh’ = upF or F tanup for non paraxial case

ECE 5616Curtis

Optical invariantaka Lagrange or Helmholtz invariant

Using the invariant, at the object (or image) of limited field diameter L: y = 0, = edge of field, u = maximum ray angle

Thus we have found the information capacity of the opticalsystem, aka the space-bandwidth product:

Rayleigh Resolution(NA = 0.6λ/Δr)

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Question

If an object that is 1 cm2 with 1 sr of solid angle is images to 2cm2 area,

What is the solid angle of this image ?

ECE 5616Curtis

Homework #2

Available at the website under homework

http://ecee.colorado.edu/~ecen4616http://ecee.colorado.edu/~ecen5616

Due in 2 weeks