OPTI-502 Optical Design and Instrmentation I John E. Greivenkamp Final Exam In Class Page 1/16 Fall, 2013 Name Closed book; closed notes. Time limit: 120 mintes. An eqation sheet is attached and can be removed. A spare ratrace sheet is also attached. Use the back sides if reqired. Assme thin lenses in air if not specified. As sal, onl the magnitde of a magnification or magnifing power ma be given. If a method of soltion is specified in the problem, that method mst be sed. Ratraces mst be done on the ratrace form. Be sre to indicate the initial conditions for or ras. Yo mst show or work and/or method of soltion in order to receive credit or partial credit for or answer. Provide or answers in a neat and orderl fashion. Onl a basic scientific calclator ma be sed. This calclator mst not have programming or graphing capabilities. An acceptable example is the TI-30 calclator. Each stdent is responsible for obtaining their own calclator. Note: On some qantities, onl the magnitde of the qantit is provided. The proper sign convention mst be applied. Distance Stdents: Please retrn the original exam onl; do not scan/fax/email an additional cop. Yor proctor shold keep a cop of the completed exam. 1) (5 points) A field lens is added to a Keplerian telescope. What is the effect of the field lens on each of the following? a) MP b) Ee Relief c) Exit Ppil Diameter d) Field of View e) Telescope Length f) Image Orientation
OPTI-502 Optical Design and Instrmentation I John E. Greivenkamp Final Exam In Class Page 2/16 Fall, 2013 2) (15 points) An aberration-free beam is focsed throgh a thick glass plate (a planeparallel plate) of thickness t in air. The plate has an index of refraction of n d and an Abbe nmber of. a) Derive an expression for the longitdinal (or axial) chromatic aberration introdced b the glass plate in terms of t, n d and The longitdinal chromatic aberration is defined to be the distance between the F and C foci. A sefl approximation to se is nn n 2 F C d Contines
OPTI-502 Optical Design and Instrmentation I John E. Greivenkamp Final Exam In Class Page 3/16 Fall, 2013 b) A thin lens of 100 mm focal length is made ot of LLF1 glass (Glass Code: 548458). A 100 mm thick glass plate is also made ot of LLF1 glass. Determine the axial chromatic aberration introdced b each of these elements. In these two sitations, is the relative order of the F and C foci the same or reversed? Lens: mm Plate: mm Order:
OPTI-502 Optical Design and Instrmentation I John E. Greivenkamp Final Exam In Class Page 4/16 Fall, 2013 3) (15 points) A moving train is being photographed b a fixed camera. The camera does not move dring the exposre. The train is at a distance of 100 m, and the focal length of the camera lens is 50 mm. The speed of the train is 10 m/s and the train motion is perpendiclar to the optical axis of the camera. a) Using reasonable approximations, what is the slowest shtter speed that can be sed so that the motion blr on the detector is 5 m? Shtter speed = sec Contines
OPTI-502 Optical Design and Instrmentation I John E. Greivenkamp Final Exam In Class Page 5/16 Fall, 2013 b) The train is being photographed on a snn da, and the detector reqires an exposre of 0.002 J/m 2 in order to prodce a good image. What f/# is shold be sed to obtain this exposre given this shtter speed? Use a tpical vale for the solar irradiance on the srface of the earth, and make an other reasonable assmptions. f/# =
OPTI-502 Optical Design and Instrmentation I John E. Greivenkamp Final Exam In Class Page 6/16 Fall, 2013 4) (25 points) A sstem is comprised of three thin lenses in air. The following partiallcompleted ratrace of the sstem is the starting point for this problem, and will be completed dring varios parts of the problem. Extra lines/ras are provided. NOTE: This problem is to be worked sing ratrace methods onl. All answers mst be determined directl from the ras o trace. The image size and location mst be determined from the marginal and chief ras associated with the object. Gassian imaging methods ma not be sed for an portion of this problem. Be sre to clearl label or ras on the ratrace form. Object EP Lens 1 Lens 2 Lens 3 XP Image Srface f t 0 1 2 3 4 5 6 100 mm -100 mm 100 mm 40 mm 60 mm Potential Chief Ra: ~ _ ~ _ 0.0 mm 0.1 0.1
OPTI-502 Optical Design and Instrmentation I John E. Greivenkamp Final Exam In Class Page 7/16 Fall, 2013 a) Which element serves as the Sstem Stop (circle one)? Lens 1 Lens 2 Lens 3 b) Determine the Entrance and Exit Ppil locations. EP: XP: Located mm to the of the first lens. Located mm to the of the third lens. c) Determine the sstem Focal Length and its Back Focal Distance (BFD). f = mm BFD = mm d) The Sstem Stop has a diameter of 20 mm. Determine the diameters of the Entrance Ppil and the Exit Ppil. Entrance Ppil Diameter = mm Exit Ppil Diameter = mm Contines
OPTI-502 Optical Design and Instrmentation I John E. Greivenkamp Final Exam In Class Page 8/16 Fall, 2013 e) For distant objects, the sstem has an nvignetted Field of View of +/- 12 deg. What is the image height in the image plane for this FOV? What are the reqired Lens Diameters to spport this FOV? Image Height = +/- mm Lens 1 Diameter = mm Lens 2 Diameter = mm Lens 3 Diameter = mm
OPTI-502 Optical Design and Instrmentation I John E. Greivenkamp Final Exam In Class Page 9/16 Fall, 2013 5) (15 points) A thick lens in air has the following specifications: R1 = -25 mm R2 = 50 mm t = 20 mm n = 1.55 A second optical sstem prodces a real image that is projected into this lens. This image serves as a virtal object for the thick lens. The virtal object has a height of +/- 5 mm and is located 15 mm to the right of the first srface of the thick lens. Determine the size and location of the image prodced b the thick lens. NOTE: This problem is to be worked sing ratrace methods onl. Two ras mst be traced: One for image location and one for image size. Gassian imaging methods ma not be sed for an portion of this problem. Be sre to clearl label or ras on the ratrace form. Contines with a ratrace form on the next page
OPTI-502 Optical Design and Instrmentation I John E. Greivenkamp Final Exam In Class Page 10/17 Fall, 2013 Srface C t n 0 1 2 3 4 5 6 t/n n n Image size = +/- mm; Located mm to the of the rear vertex.
OPTI-502 Optical Design and Instrmentation I John E. Greivenkamp Final Exam In Class Page 11/16 Fall, 2013 6) (10 points) This diagram shows an optical sstem consisting of two refracting srfaces and an object. Also shown are the locations and sizes of the stop, the entrance ppil (EP) and the exit ppil (XP). Show the paths of the marginal and chief ras throgh the sstem along with the location and size of the image. No calclations or eqations are reqired or allowed. Please se a straight edge! z EP L2 Stop L1 XP Object
OPTI-502 Optical Design and Instrmentation I John E. Greivenkamp Final Exam In Class Page 12/16 Fall, 2013 7) (20 points) Two thick lenses in air are combined into a single imaging sstem. Both lenses are 25 mm thick and both lenses have a focal length of 100 mm, however the index of the first lens is 1.6 and the index of the second lens is 1.5. The vertex-to-vertex spacing of the lenses is 50 mm. The principal plane locations for the two individal lenses with respect to srface vertices are shown in the figre. All nits are in mm. A 20 mm diameter stop is located between the two thick lenses. The stop is 20 mm to the right of the rear vertex of the first lens. The vertex-to-vertex separation of the two lenses is 50 mm. All nits are in mm. f 1 = 100 t 1 = 25 n 1 = 1.6 DSTOP 20 mm f 2 = 100 t 2 = 25 n 2 = 1.5 9.38 P 1 P 1-6.90 9.84 P2 P 2-7.58 z 20 30 a) For this sstem of two thick lenses, determine: Sstem Focal Length Location of the Rear Principal Plane of the sstem relative to the rear vertex of the second lens Back Focal Distance b) Determine the entrance ppil and exit ppil locations and diameters. The entrance ppil is to be located relative to the front vertex of the first lens, and the exit ppil is to be located relative to the rear vertex of the second lens. NOTE: Onl Gassian methods ma be sed for this problem. Sstem Focal Length = mm BFD = mm Sstem P': Located mm to the of the rear vertex of the second lens. EP: D EP = mm; of the first lens. XP: D XP = mm; the second lens. Located mm to the of the front vertex Located mm to the of the rear vertex of
OPTI-502 Optical Design and Instrmentation I John E. Greivenkamp Final Exam In Class Page 13/16 Fall, 2013 Method of Soltion: Contines
OPTI-502 Optical Design and Instrmentation I John E. Greivenkamp Final Exam In Class Page 14/16 Fall, 2013
OPTI-502 Optical Design and Instrmentation I John E. Greivenkamp Final Exam In Class Page 15/16 Fall, 2013 Spare ratrace forms: Srface C t n 0 1 2 3 4 5 6 t/n n n Srface f 0 1 2 3 4 5 6 t
OPTI-502 Optical Design and Instrmentation I John E. Greivenkamp Final Exam In Class Page 16/16 Fall, 2013 Srface 0 1 2 3 4 5 6 f t
OPTI-502 Eqation Sheet OPL = nl n sin θ = n sin θ 1 1 2 2 γ= 2α n 1 d= t = t τ n φ= (n n)c n n = +φ z z f 1 f f R φ n n F E = = = z/n ω m = = z/n ω m f f = = f f n m= m n m N F2 2 R1 1 n = n 2 Δz/n = mm Δz/n PN = PN= f + f F 1 2 R t τ = ω= n n φ =φ 1+φ2 φφ 1 2τ d φ n φ 1 δ = = τ d n φ φ 2 δ = = τ ω =ω φ = +ωτ f/# f BFD = d + f R FFD = d + f F E NA n sin U n DEP 1 1 f/# W ( 1 m) f/# 2NA 2n I = H = n n = tan( θ 1/2) 10in 250mm MP = = f f 1 MP = m mv = mobjmpeye
M ρe L = = π π A Φ= LAΩ Ω 2 d πlo E = 2 4(f /# ) W Exposre = E Δ T a + Un a = and a Half a and a Fll DOF =± B f /# W L H fd LH = L B NEAR = 2 δ = ( n 1) α δ ε = ν = P Δ Δ α 1 ν = δ ν ν 1 1 1 2 nd1 1 α 1 ν = δ ν ν ε δ 2 2 1 2 nd2 1 P P 1 2 = ν1 ν2 ( α δmin ) sin ( α / 2) sin / 2 n = 1 n S θ C = sin nr D= 2.44λ f /# D f /# in μ m 2 Sag 2R nd 1 ν= n n n F n C d C P = n F n C δφ δf 1 = = φ f ν TA CH rp = ν φ1 ν1 φ2 ν2 = = φ ν ν φ ν ν 1 2 1 2 δφdc δfcd ΔP = = φ f Δν