OPTI-503 OpticalDesignandInstrumentation II Midterm Exam In Class Pagell12
JohnE. Greivenkamp Spring2014
So\.,ll.'*,
Name
Closedbook; closednotes. Time limit: 75 minutes. An equationsheetis attachedand can be removed. Use the back sidesif required. If a methodof solutionis specifiedin the problem,that methodmust be used. You must show your work and/or method of solutionin order to receive credit or partial credit for your answer. Only a basic scientif,rccalculatormay be used. This calculatormust not have programmingor graphingcapabilities.An acceptableexampleis the TI-30 calculator. Each studentis responsiblefor obtainingtheir own calculator. DistanceStudents:Pleasereturnthe original exam only; do not scan/FA)Uemailan additionalcopy. Your proctor shouldkeep a copy of the completedexam.
l) (10 points) An fl3 systemhas fifth-order sphericalaberration,and Wooo: -8.0 pm. Determinethe axial separationbetweenparaxialfocus and marginalfocus. Marginal focus is wherethe marginal ray (p : 1.0 zoneof the pupil) crossesthe axis.
t^*J -- \);,o,- Pt f^
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+
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+
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ft
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AU¿r¡
= -3
e..¿o
= |TZB
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- 8ru^
-_ 2ir*n
Se = g (cl*)tau¿,¡ 5¿
.
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OPTI-503 Optical Design and InstrumentationII Midterm Exam - In Class Page2ll2
John E. Greivenkamp Spring2014
2) (20 points) A systemhas sphericalaberrationWo¿obalancedwith defocusÄWzo in order to obtain the condition of Minimum V/avefront Variance. Determinethe RMS wavefront error that is presentin this situation.
W = LWzop'*W*opo
(w) --
Ï'[ ¡ø.rl,
p' * truopo)ndo de
-lo*,,*!r*, (w) (w)'=Ior:,* T*å,* ! nw,ow*o pdpdo (*') =+'[i(or,,o'*w*opu)' p' +2LW,ow*oou)o dpd.0 (or:,r' +w&o (*') = +'Íi
(r'l =lo*:,*Ir:^,* )tw,ow*o o' =(*'l - (w)'=i¡r:, *
* *r:^, ltw,ow*o
Find the minimumbv differentiation: ôo2
I --- l--= . LWro+;W*o -0 ôLWro 6 6 LWro- -W*o This is the condition for mid-focus or minimum wavefront variance. Continues...
OPTI-503 OpticalDesignandlnstrumentation II MÍdtermExam In Class Page3ll2
JohnE. Greivenkamp Spring2014
Substitutethis resultinto the generalexpressionfor the wavefrontvariance:
o2=(r') - (w)'= * i.or:,
*r:,,
*lnw^wooo
o' = * o.oo555 5wfoo irA, *r:^, IrA,=
o'=Yfu 180 D[/
RMS:JJ _ " o4o- 0.0745w"^ " " 040 13.4
Notethatthis resultis whatwasnotedin the classnotesastheratioof the PV andRMS wavefronterrorsfor SphericalAberration.
OPTI-503 Optical Designand lnstrumentationII Midterm Exam - In Class Page4lI2
John E. Greivenkamp Spring2014
3) (15 points) Tangentialoblique sphericalaberrationísWzqz. a) Give the expressionfor the wavefront error W for this aberration.
("J __ w.*.
Ã. f*
.., s. ê
b) Derive the expressionsfor the transverseray aberrationse, and e* for this aberration. Leave the results in terms of xo and yo.
(tre'*'3r-)
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r^J = u¿*ta t{' ( të
h fr" z - +')"*' H' (++î + 2t"*')
tg
+rË" è Tu..*rn'(2*exÐ
t.ç
c) Usingtheseresults,write downtheexpressions for thetangentialandsagittalray fans. (¿ Z
To ^¡=..ti .t
4
t' .E
(fn
S
=
f,- ". tle= <' ) 4t ? * -r '-Þ- .L
6,'
Ltt^, -3 df
"7e=o)
Ò
Continues...
oPTr-503
Optical Design and lnstrumentationII Midterm Exam In Class Page5l12
John E. Greivenkamp
Spring2014
d) Sketchthe ruy fans for this aberrationat H = 0, H: 0.7 and H : I . Be sureto label the plots and includeunits. Assumean f/4 systemwith'W2a2: 5 pm.
H= I
[=i ct.¡. - &?¿"&-1. (¡nq
[-t :
-
¿Lit¿e$¡ì$-.1.
S g [.c.-'.< -0 .b.tr-¿*rt*
(z
t/'f,
?, 2 z &/k = ?
rx , l,7l
- 1(¡) :o
(<^-)
h' ,ff
= l¿-n
Q "t.
= -/r,o H?"'
OPTI-503 OpticalDesignandlnstrumentation II Midterm Exam In Class Pase6112
JohnE. Greivenkamp Spring2014
4) (20 points) You are given the following set of ray fans. The ray fans areplotted at H : 0 and H : 1.0 for an f/4 system. The dashedlines indicatethe slopeof the rayfans through the origin. Cnly first and third order aberrationsare present. Calculatethe aberrationcoefficients Wxyz for eachaberration. The units on the plots are microns. H:l 120
ey(w)
't20
100
100
80
80
60
60
40
40
20
20
yp
-20
0 -20
-40
-40
-60
-ou
-80
-80
-100
-100
-120
-120
H:0 120
ey(um)
120
100
100
80
BO
60 40
60
_____10____
40
20
20
-¿u
-20
-40
-40
-60
-60
-80
-80
-100
-t00
-120
-120
0
-T¿
Blankpageþllows...
OPTI-503 OpticalDesignandInstrumentation II Midterm Exam In Class PageTlLZ
JohnE. Greivenkamp Spring2014
Because only H : 0 andH = I aregiven,it is not possibleto distinguish betweentilt or distortion.
ft4
4=s rP
Tilt (or Distortion): y-fan offset at the origin (H: 1) R e r ( ! , = 0 ;H - 1 )= -: L WtrH= -I6pm
LW r ,= 2.0Pm
rP
Defocus: x-fan slopeat the origin (H:0) eor(x,= I; H-
0) = -Z! nWro= -72pm
LWro= 4.5pm
rP
Aberration:x-fanhasSA anddefocusat H = 0 Spherical
€ x ( x p = 1 ; H - 0 ) =- 2 R L W r o - 4 L w * o = 4 0 p m
wuo=1.5w
rP
rP
Field Curvature: x-fan slope at the origin (H = 1)
eï@r=T;H-l)= -zLtwro-zlwuollz =-28/tm rP
wrro=-2.75¡tm
rP
Astigmatism:y-fanslopeat theorigin(includetilt offset)(H : 1)
=r;H - 1)= -L or,,, -z! nw^-2R wrroH'-2R wrrrH'= -rl2pm €|,(yp rP
rP
rP
rP
Wrr,= 4.25pm Coma:all terms(H: l)
€ r ( r ,= l ; H - 1 )= - ^ o r , , H - 2 L o r r o - 4 R w o o o - 2 L w r r o H ' - z L w r r r H ' rP
rP
-3 R wrrrH=-4opm rP
rP
rP
rP
4z' =l'666¡tm
OPTI-503 Optical Designand InstrumentationII Page8lI2 Midterm Exam In Class
John E. Greivenkamp Spring2014
5) (20 points) You are given the following set of WAVE fans. The wave fans are plotted at H : 0 and H : 1.0 for an fl5 system. Only third order aberrations(spherical aberration,field curvature,astigmatismand coma) are present. There is no defocus,tilt or distortion. Calculatethe aberrationcoefficients'Wxyzfor eachaberration.The units on the plots aremicrons. H:l
w (pm)
o
5 4
2 1
a
,Yp
0 - l
-¿
-z -J
-4
-o
H:0 o
5 4
4
.t
3
¿
2
1
1 0
t Y p
I
-z -J
-J
-4
-4
-5
-5
-o
-o
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OPTI-503 OpticalDesignandInstrumentation II JohnE. Greivenkamp MidtermExam In Class Page9ll2 Spring 2014 +1"-
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Midterm Exam- In Class
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John E. Greivenkamp Spring2014
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OPTI-503 Optical Designand lnstrumentationII Midterm Exam - In Class Page11112
John E. Greivenkamp Spring2014
6) (10 points) Miscellaneous items... a) What is the cutoff frequencyfor a diffraction limited system.
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b) A systemhas2 wavesPV of wavefronterror due to defocus.V/hat is the approximate RMS wavefront error?
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[:,*,** 3.<
patch? c) Whatis anisoplanatic A
l e Íì.,-.
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if the to be well corrected d) Accordingto theMaréchalCriterion,a systemis considered StrehlRatiois sreaterthanwhatvalue?
SC
e) What is the relationshipbefweenthe PSF and the MTF of a system?
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oPTr-503 Optical Designand InstrumentationII Midterm Exam - In Class Page12/12
John E. Greivenkamp Spring2014
7) (5 Points) A systemhasthird order astigmatismand field curvatureonly. a) What is the relative order of the Medial, Petzval,Tangential and Sagittal surfaces?
T-r¡Se
?Sl1f
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e6--llv Ëfl.-.( b) At eachof thesesurfaces,sketchthe appearance of the geometricalspot diagams. Pleasemaintainan approximatelyconstantscalebetweenyour four sketches.
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