REU/RET Optics Research Workshop 2014 Workshop #1 Excel Spreadsheets and Data Analysis

REU/RETOptics Research Workshop 2014

Workshop #1Excel Spreadsheetsand Data Analysis

Dr. Mike NofzigerProfessor

College of Optical SciencesUniversity of Arizona

Dr. Mike Nofziger 2014

Optics Research Workshop (ORW) Curriculum

“These Optics Research Workshops are designed to teach participants basic opto-electronic laboratory techniques, through hands-on measurements and experiments with lasers, fiber optics, solar cells, spectroscopy, lighting, imaging, data analysis, electronics, etc. Topics and hardware have been chosen to provide a background to common lab practices that participants will (likely) see and use during their summer research experiences!

Emphasis will be placed on the practical vs. theoretical aspects of lab practices and techniques. Whenever possible, we will stress applications of hardware to real-world laboratory situations.” In the process, participants will gain hands-on experience with some of the basic and most useful lab techniques most important in an optics lab.

RET participants (especially) will learn ideas about teaching optics in their classrooms.

All of us will explore ways to integrate optical sciences with Native American cultures.

Dr. Mike Nofziger 2014Workshop 1-1

Workshop #1 Outline: ● What is Optics and Optical Engineering? “Optics Is…” ● What is Light? ● Basics of Excel Spreadsheets and Data Analysis

- Using Excel- Analyzing Data

- mean (average)- median- variance- standard deviation

- Plotting Data- linear/linear plot- linear/log plot- log/log plot- error bars- “trendlines” (i.e. curve-fitting)- histograms


OPTICS IS…

OPTICS IS…BIG

The UofA Steward Observatory Mirror Lab casts mirrors up to 8.5 meters in diameter.

OPTICS IS…SMALL

Micro-lenses are now made with diameters as small as ≈ 10 μm. Arrays of micro-lenses are used on the CCD sensors of many digital cameras.

OPTICS IS…HOT

National Ignition Facility at Lawrence Livermore will

deposit 1.8MJ in 2 nanosec onto a 2 mm diameter tritium target,

heating it to 100,000,000K

OPTICS IS…COOL

Laser cooling and trapping at OSC can

capture and slow down individual atoms until

their effective temperature is <1 μK.

OPTICS IS…FAST

A 9 micron fiber can carry data at a rate of 10 Gbit/sec. Using dense wavelength-division multiplexing (DWDM, 16 wavelengths), 2,000,000

simultaneous phone conversations can be transmitted

through a single fiber.

OPTICS IS…SLOW

Using a new process, it now takes “only” 27 days to grow KDP crystals to this size for frequency

multiplication (It used to take 1 year!)

OPTICS IS…NEAR

Scanning tunneling microscopy (STM) at OSC

can resolve individual molucules (like these three

C-60 “buckyballs”).

OPTICS IS…FAR

UofA NICMOS on Hubble Space Telescope found

this galaxy 12 billion light years distant. OSC contributions to HST

include discovery of the original out-of-focus

problems.

OPTICS IS…NIGHT

A Gen III image intensifier can produce a useful

image under starlight. You can see a 6’ tall man at a

distance of 580 yards.

OPTICS IS…DAY

The sulfur lamp, the size of a golf ball, produces nearly 100 times as much light as a conventional HID lamp,

nearly 1000 times as much as a 40 watt tungsten

lamp.

OPTICS IS…NEW

LED’s are now available in three primary colors (great

for displays) and in white for illumination.

A violet laser diode (406nm) is a recent introduction;

expect smaller spot sizes and denser data storage.

OPTICS IS…OLD

In 1609, Galileo built a telescope based on an

earlier design and used it to discover four of Jupiter’s

moons.

▪ Communications▪ Medical Equipment/Procedures and Life Sciences ▪ Computers and Data Storage ▪ Military ▪ Telescopes and Satellites ▪ Cameras and Image Capture Devices ▪ Custom Illumination ▪ Industrial Manufacturing ▪ Metrology ▪ Nanotechnology and MEMS ▪ Research and Education

… EVERYWHERE!!!

OPTICS IS…


“The Nature of Light” Quantum Mechanics Physical Optics Geometrical Optics

EXAMPLE: Young’s Double Slit

Light is energy, transported from one locationto another via electromagnetic (EM) waves.


Characteristics of an EM wave:

• EM waves are transverse waves (the electric field oscillates in a plane perpendicular to the direction of

travel).

• speed c (speed of light in vacuum, universally-accepted symbol)• frequency ν “nu”• wavelength λ “lambda”• amplitude• polarization• phase


EM wave—Speed, Frequency, and Wavelength

c = ν λ

Electromagnetic Spectrum

81 0 71 0 61 0 51 0 41 0 31 0 21 0 1 0 11 0 - 21 0 - 31 0 - 41 0 - 51 0 - 61 0 - 71 0 - 81 0 - 91 0 - 101 0 - 1 11 0 - 121 0 - 1 31 0 - 141 0 - 151 0 - 1 61 0 -1

700 600 500 400

W a v e le n g th ( in n a n o m e te rs)

V is ib le s p e c tru m

W a v e le n g th (m )

F req u e n c y (H z )1 0 21 0 31 0 41 0 51 0 61 0 71 0 810 91 0 1010 111 0 121 0 131 0 141 0 151 0 1610 1710 1810 1910 201 0 211 0 2210 231 0 2410

R a d io w a v e s X ra y s G a m m a ra y s

c = 299,792,458 m/sec. in vacuumc ≈ 300,000,000 m/sec. = 3x108 m/sc ≈ 186,000 miles/s


► NYC to LA ≈ 1/62 sec. (62 trips in one second!!)► sun-to-earth ≈ 8 min.► Earth-to-Mars = 9-16 min. (depending on where Mars is)► Proxima Centauri-to-earth = 4.3 years

(Proxima Centauri is the closest star to our own sun, 4.3 light-years away)► A light-year is defined as the distance light travels (in the vacuum of outer space)

in one year:

EM wave—Speed of Light in vacuum (or ≈ in air)


Hubble eXtreme Deep Field (XDF) image shows:

▪ galaxies 13.2 billion light years distant

(galaxies that are 13.2 billion years old)

EM wave—Speed of Light in glass


► Light traveling through a media like glass has a slower velocity than in air. The frequency is the same (constant) but the velocity is slower.

► vm < c

► n ≡ c/vm ; vm = c/n

where n ≡ Refractive Index and c = speed of light in air

► n ≥ 1 for any material; n = 1.5 for a typical type of optical glass

• water 1.33333• glass 1.46 to 1.76 (typically 1.5 is used)• plastic 1.4• air 1.0• Oil 1.6• Diamond 2.42• Germanium 4• Silicon 3.4

Refractive Index of Different Materials

► A graph of refractive index vs. wavelengthis called a dispersion curve:


Basics of Data Analysis:

● Mean (average) of a sample population Sample Mean

Example: (1,2,3,4,5,6,7,8,9,10)


1 2 3

1

...

1

N

N

ii

x x x xxN

x xN

1 2 3 4 5 6 7 8 9 10 55 5.510 10

x

Basics of Data Analysis: In Excel

● Sample Mean


=(A1+A2+A3+A4+A5+A6+A7+A8+A9+A10)/10

=SUM(A1:A10)/COUNT(A1:A10)

=AVERAGE(A1:A10)

A B1 12 23 34 45 56 67 78 89 9

10 1011 Average = 5.512 Average = 5.513 Average = 5.5


● Sample Variance

Example: (1,2,3,4,5,6,7,8,9,10)

(1)

(2)


1 2 3 4 5 6 7 8 9 10 55 5.510 10

x

22

1

11

N

ii

x xN

2 2 2 2 2

22 2 2 2 2 2

1 5.5 2 5.5 3 5.5 4 5.5 5 5.5110 1 6 5.5 7 5.5 8 5.5 9 5.5 10 5.5 1 5.5

2 9.167


● Sample Standard Deviation

Example: (1,2,3,4,5,6,7,8,9,10)

(1)

(2)

(3)


1 2 3 4 5 6 7 8 9 10 55 5.510 10

x

2

1

11

N

ii

x xN

2 2 2 2 2

22 2 2 2 2 2

1 5.5 2 5.5 3 5.5 4 5.5 5 5.5110 1 6 5.5 7 5.5 8 5.5 9 5.5 10 5.5 1 5.5

2 9.167 3.028

Plotting Data: In Excel

● Linear-Linear


(1) 0 ; " "y mx b x y x

0 10 20 30 40 50 60 70 80 90 1000

102030405060708090

100

y = x

x

y

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 20

0.20.40.60.8

11.21.41.61.8

2f(x) = xR² = 1

log(y) vs. log(x)

log (x)

log (y)

● Log-Log 10 10log logy x


● Linear-Linear


2y x

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 20

0.51

1.52

2.53

3.54

f(x) = 2 xR² = 1

log (y) vs. log (x)

log (x)

log (y)

● Log-Log

0 10 20 30 40 50 60 70 80 90 1000

100020003000400050006000700080009000

10000

y = x2

x

y log 2logy x


● Linear-Linear


3y x

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 20

1

2

3

4

5

6f(x) = 3 xR² = 1

log (y) vs. log (x)

log (x)

log (y)

● Log-Log

0 10 20 30 40 50 60 70 80 90 1000

100000200000300000400000500000600000700000800000900000

1000000

y = x3

x

y log 3logy x


● Linear-Linear


2 3and andy x y x y x

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 20

1

2

3

4

5

6

log (y) vs. log (x)

log (x)

log (y)

0 10 20 30 40 50 60 70 80 90 1000

100000200000300000400000500000600000700000800000900000

1000000

y = x

x

y

Computer Exercises: In Excel

● Michelson’s “Speed of Light” Data Set (measured values of “c”)- Find the mean, variance, and standard deviation of his values- Plot histograms of his data- Plot a “best-fit” Gaussian distribution

=NORMDIST(x, mean, standard dev, FALSE)

● “Old Faithful Eruptions” Data Set- Plot histograms of the data


REU/RET Optics Research Workshop 2014 Workshop #1 Excel Spreadsheets and Data Analysis

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