ECSE 423/ XXXXXXXXXXAssignment 2 2. Ray matices: The figure below shows a Cooke triplet, which was firstdesigned in 1883 and whichwas the first lens to allow the elimination of most distortion at the...

ECSE 423/527 2020 Assignment 2
2. Ray matices: The figure below shows a Cooke triplet, which was firstdesigned in 1883 and whichwas the first lens to allow the elimination of most distortion at the edge ofthe field of view. It canadditionally correct all other first order aberrations (which we will studylater in the course).Although it was invented many years ago, this design still forms the basis ofmany simple lenssystems found in cell phone cameras for example. In this problem we willanalyse a simplifiedversion of the triplet, where we will assume that the first and last lenseshave identical positivefocal lengths (f1) , the second lens has focal length f2 and that the twospacings t are identical. Alllenses are thin lenses.
i) Derive the ABCD matrix for this system (ignoring object and imagedistances). Note thatthroughout this problem you are permitted to use symbolic maths software (suchasMathematica or MATLAB) to help you derive solutions) [6 points]
ii) Obtain expressions for the effective focal length and back focallength [4 points]
iii) Using the expression for effective focal length f, obtain anexpression for focal length f2 as afunction of f and t [4 points]
iv) Assuming that the lens has an effective focal length of 100 mm,plot the following graphs:
a. Focal length f2 as a function of t for focal length f1 = 25, 50 and 75mm, over the ranget=0,50 mm [3 points]
b. bfl as a function of t for focal length f1 = 25, 50 and 75 mm, over therange t=0,50 mm[3 points]
v) From the expression for f2 and guided by the graphs, obtain anexpression for themaximum possible value of spacing t as a function of f and f1. [4 points]
vi) In looking at the graphs, and taking into account ease ofmanufacturing and performance,how would you select a suitable value of f1 and t within the available range?[4 points]
vii) Assume that the effective focal is 100 mm, f1 is 50 mm and t is20 mm. What should be thevalue for f2?[2 points]
[30 points total]
Oct 06, 2021
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