OPT287, MTH287
Due: Fri. Apr. 5, 5pm, Wilmot 213
Homework 6
1.
Recall that the formula for the Fourier coefficients of a periodic function is
x + 2
cm =
i
1 0
f (x)e
x 0 2
2 mx
dx .
Calculate these coefficients for the following functions:
a)
b)
c)
d)
In
OPT287, MTH287 Due: Mon. Apr. 15, 5pm, W 213
Homework 7
1.
Recall that the formula for the Fourier transform is given by
1
f ( p) =
2
f (x)eipx dx .
Calculate the Fourier transforms of the following functions
f
1/a
x
-a/2
a)
a/2
f
1
x
-a
b)
c)
a
f (x) = e
Optics 444
Homework #2
Due: Thursday, January 28, 2016
1) A HeNe (632.8 nm) interferometer is set up in a manufacturing facility to test the quality of
polished surfaces using the following doublet objective lens. To properly test the surface, the
doublet
Optics 444 - Lens Design
Homework #1
Due: Thursday, January 21, 2016
1. Standard Homework Output (SHO):
a) Open the CodeV sample lens dbgauss.len.
b) Use the Scale option under the Edit menu to scale the focal length of your lens to 50 mm.
c) Change the a
OPT287, MTH287
Due: Wed. March 6, 5pm, Wilmot 213
Homework 4
1.
Solve the following integrals using residues:
a)
(x
2
b)
x
dx
,
+1
4
c)
(x
2
d)
2
dx
, for a > 0, b > 0.
+ a )(x 2 + b 2 )
2
1
a + sin d , for a > 1.
2
0
2
e)
dx
,
+ 4) 2
d
tan 3i d .
0
I
Optics 444
Homework #4
Due: Thursday, February 11, 2016
20:06:45
1) Use the procedure below to design a single element Landscape lens for a disposable box camera with
a focal length of 50 mm, F/10, and a half field of view of 22 degrees. The glass is NBK7
OPT287, MTH287
Due: Mon. April 22, 5pm, Wilmot 213
Homework 8
1.
Find the following Hilbert transforms (assuming k real):
a)
sin kx ,
b)
x
,
1+ x 2
c)
1
.
1+ x 4
2.
Calculate the local impulse response of a Lorentz-model dielectric, i.e. the timedomain fo
Optics 444
Homework #6: Doublet Design
Due: Thursday, March 24, 2016
1. Use the procedure below to design an F/1.4 objective out of Germanium that is corrected
(aberrations are minimized but not necessarily zero) for both chromatic aberration and
spherica
OPT287, MTH287
Due: Thu. Jan. 31, 11:05, at the start of the lecture.
Homework 1
1.
Find i) the real part, ii) the imaginary part, iii) the absolute value, iv) the
argument, and v) the complex conjugate of:
a) z 2 , first in terms of both x and y and then
Optics 444
Homework #7 Triplet Designs
Due: Thursday, March 31, 2016
1. Goal: design a 50 mm focal length, F/8 visible objective lens with a 20 degree half field of
view with no vignetting (other than that introduced by pupil aberrations) using an air spa
OPT287, MTH287
Due: Fri. Feb. 14, at the beginning of class
Homework 2
1.
Consider the sum of two counter-propagating monochromatic waves in 1D:
A(x,t) = cos(kx t) + cos(kx + t) .
(i)
a)
Show by using angle sum and difference formulas (or you can also use
OPT287, MTH287
Due: Mon. April 1, 5pm, Wilmot 213
Homework 5
1.
Solve the following integrals:
2
a)
P
0
1
d , for 1 < a < 1,
a + cos
b)
(x 2 + a 2 )
dx , for a, b, c > 0,
2
2 2
2
2
(x + b ) (x c )
P
c)
d)
cos(kx) dx
, for k real,
2
+ a2 )3
(x
e)
2
! si
The following code is used for both part a) and b).
function hw4_1a
T=(1000:1:10000);
V_lamda=[0.0004, 0.0012, 0.0040, 0.0116,.
0.0230, 0.0380, 0.0600, 0.0910, 0.1390,.
0.2080, 0.3230, 0.5030, 0.7100, 0.8620,.
0.9540, 0.9950, 0.9950, 0.9520, 0.8700,.
0.75
Chapter 1
Introduction to Radiometry
1.1 Definitions
Consider the following definitions a starting point for our study of radiometry:
radio- [<L. radius] a combining form meaning ray, raylike
-metry [Gr. -metria < metron] a terminal combining form meaning
Important Dates & Announcements
Exam 1 (10%) October 1
Exam 2 (20%) November 5
Exam 3 (20%) December 10
Poster Session (Goergen 108) December 11, 3:30 pm
First Monday workshops are next week. No Tuesday/Wednesday
workshops next week.
Tuesdays lecture will
Important Dates & Announcements
Exam 1 (10%) October 1
Exam 2 (20%) November 5
Exam 3 (20%) December 10
Poster Session (Goergen 108) December 11, 3:30 pm
If you havent signed up for a workshop, do so immediately.
Workshops on Tuesday/Wednesday this week w
Introduction to Optics
Optics 101
Prof. Thomas Brown
Tues-Thur 12:30 pm
Meliora 221
Course Information
Weekly workshops (10-15 students)
Lectures
Group Project
Homework
Exams
Grading
Homework
Group Project*
Exams
40%
10%
50%
*Poster Session December 12
Im
Important Dates & Announcements
Exam 1 (10%)
Exam 2 (20%)
Exam 3 (20%)
Poster Session
October 1
November 5
December 10
December 11, 3:30 pm
If you havent signed up for a workshop, do so immediately.
No workshops Monday next week.
Workshops on Tuesday/Wedn
1
Optics 101
Optical materials
What is an optical material?
What happens when light passes through a material?
delay/dispersion (refractive index)
scattering
absorption (Beers Law)
Types of materials
Optics 101 Lecture #6
T. G. Brown
09/17/2015
Light and
Optics 101 Homework 4
Due at 12:30 pm on October 29
!
Problems 1& 2 are mirror problems. The best approach is to usually do the following:
i) Find the curvature of the mirror (1/R). ii) Use this to find the power of the mirror: =-2c.
iii) Then use the len
Optics 101
Homework 3
Due by 12:30 on Tuesday Sept 29
1. Take a photograph of the moon with a ruler in the image field.
a)
Work with a friend or classmate to hold the ruler at a known distance (for example, 25 cm)
in the image field so that you are photog
!
Optics 101
Homework 1
Due at 12:30 pm on Sept 15, 2015
1. Short calculations: You may need to look up some of the information on the internet or in a
reference book. When you do so, provide the complete reference.
a) Find the frequency, in THz (terahert
!
Optics 101
Homework 2
Due at 12:30 pm on Sept 22, 2015
1. How much time does it take light (wavelength 1500 nm) to travel 10 mm
a) in air? b) in glass having a refractive index of 1.52? c) in silicon (n = 3.5)
!
2. Getting acquainted with an optics cata
!
1.
a)
b)
c)
d)
e)
!
Optics 101
Example Test
(25 pts) Define the following (give units, where appropriate) -Dispersion
Virtual Image
Irradiance
Radiant Intensity
Solar Spectral Density
Multiple Choice (3 pts each)
2. The dispersion of an optical material
!
Optics 101 Glossary
!
Absorption - For a propagating wave, the process by which optical power or irradiance
decreases on propagation; it can also refer to the fraction of optical energy converted to
electronic or thermal energy in a material as light pa
Optics 287, Math 287 March 19, 2009 11:05 to 12:20
Midterm Exam
1. a) Calculate the gradient, divergence or curl (whichever applies) of
A (r ) = r r ,
n
where n is an integer. (15 pts.) b) For what values of n is the divergence constant? (5 pts.) c) For w