OPTI-202R Final Exam Name Spring 2008

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1 OPTI-202R Final Exam Name Spring 2008 Note: Closed book; closed notes. Eqation sheets are inclded. A spare ratrace sheet is also attached. Assme thin lenses in air if not specified. If a method of soltion is specified in the problem, it mst be sed. No pre-stored programs in or calclator ma be sed. Yo mst show or work and/or method of soltion in order to receive credit or partial credit for or answer. 1) (25 points) Yo are sing a camera with a 20 mm focal length lens to take a pictre on large-format solid state detector (total image size is 23.7 mm x 15.6 mm). The long dimension of the detector is oriented horizontall. Yo are photographing a hose against a distant montain backdrop, and the distance to the hose is 15 m. The camera is focsed on the hose. The hose is 10 m wide and has a peaked roof that is 8 m high. Assme that the lens is a thin lens with the stop at the lens. 8 m 10 m a) (5 points) How far behind the lens mst the detector be located? How big is the image of the hose on the detector? Sketch the image formed on the detector (as seen throgh the back of the sensor). Detector Lens-detector separation = mm 15.6 mm Image size: mm x mm 23.7 mm 1/18

2 b) (5 points) What is the horizontal Field of View of this photographic sstem (in degrees)? FOV = +/- degrees c) (5 points) The pixels on the sensor are 7 μm sqare. If this is the limiting image blr in the sstem, what is the fastest f/# lens that can be sed so that the distant montains are also considered to be in focs along with the hose? Remember that the camera is focsed on the hose. f/# = _f/ With this f/#, what is the closest object that will be considered to be in focs? The closest in-focs object is m from the camera. 2/18

3 d) (5points) It is a overcast da (otdoor illminance = 10 3 lx = 10 3 lm/m 2 ). The reflectance of the hose is ρ = 0.5 and the montains have an average reflectance of ρ = What is the image plane illminance for the hose and the montains? Illminance (Hose) = lm/m 2 Illminance (Montains) = lm/m 2 e) (5 points) The sensor has an effective ISO# of 100. What is the reqired exposre time for the image of the montains to be properl exposed? 2 Exposre: HV ( lm-s/m ) 0.8 = ISO # Exposre time = sec 3/18

4 2) (25 points) An optical sstem consists of two thick lenses in air with a stop between the lenses as shown. The diameter of the stop is 20 mm. All of the radii of crvatre are 100 mm. Use the diagram to determine the sign for each srface radis of crvatre. The index of the first lens is 1.5, and the index of the second lens is 1.7 n = 1.5 n = mm 25 mm 25 mm 15 mm This problem is to be worked sing ratrace methods onl. Gassian imaging methods ma not be sed for an portion of this problem. For grading prposes, the vales for or final ras mst be entered into the ratrace sheets that follow. Use a separate ratrace sheet for the marginal ra and the chief ra. Be sre to clearl label or ras, and note which ra is sed to determine each answer. a) (5 points) Determine the locations of the entrance and exit ppils. Entrance Ppil: mm to the of the first srface. Exit Ppil: mm to the of the last srface. 4/18

5 5/18 Marginal Ra

6 6/18 Chief Ra

7 b) (5 points) Determine the focal length and back focal distance of this optical sstem. f = mm BFD = mm c) (5 points) Determine the diameters of the Entrance and Exit Ppils. Entrance Ppil Diameter = mm Exit Ppil Diameter = mm 7/18

8 d) (5 points) The sstem has a Field of View of +/- 10 degrees. What is the image height corresponding to this FOV? Image Height = +/- mm e) (5 points) What are the reqired diameters for lenses 1 and 2 for this sstem to be nvignetted over this FOV? Both srfaces of each lens will have the same diameter. D1 = mm D2 = mm 8/18

9 3) (25 points) A common laborator practice is to create a finite-conjgate imaging sstem b combining two lenses that are designed for infinite conjgates. The two lenses are placed nose-to-nose, so that both lenses are sed at their design conjgates. An object placed at the focal point of the first lens is imaged to the focal point of the second lens. f 1 f 2 F 1 F Lens 1 Lens 2 2 a) (5 points) What is the lateral magnification associated with this imaging? Please provide a derivation of or reslt, and it mst be valid for an separation between the two lens sstems. Eqation: m = 9/18

10 b) (5 points) For most lenses, a reasonable representation of this sstem is to model each lens assembl as a thin lens with its stop at the lens. Becase of the actal elements and monts of the lens, there will be some phsical separation between the two thin lenses. f 1 f 2 F 1 t F 2 The tpical first instinct for this design is to make the diameters of the two thin lenses (or the apertres at the thin lenses) the same diameter. D 1 = D 2 What is the major problem with this approach? Hint: consider the sstem performance with an extended object (h 0). 10/18

11 c) (7 points) To fix this problem, the lens apertres shold be of different size. Let s arbitraril make the first apertre smaller than the second. Sstem specifics: f 1 = 100 mm D 1 = 10 mm f 2 = 50 mm t = 80 mm Object size = +/- 20 mm What is the reqired diameter of the second thin lens D 2 for the sstem to be nvignetted for this object? Sketch the sstem, showing the diameter of the second lens along with the marginal and chief ras Srface f φ t Sketch: D 2 = mm f 1 f 2 F 1 t F 2 11/18

12 d) (8 points) An even better soltion is to place a new stop halfwa between the two lens assemblies. The new sstem specification: f 1 = 100 mm f 2 = 50 mm t 1 = 40 mm Stop Diameter = 10 mm t 2 = 40 mm Object size = +/- 20 mm Determine the reqired lens diameters for the sstem to be nvignetted for this object. Srface f φ t D 1 = mm D 2 = mm 12/18

13 4) (15 points) An imaging sstem consists of two separated thin lenses in air: f 1 = 100 mm f 2 = 50 mm t = 80 mm a) (8 points) Determine the stop location reqired to make the sstem telecentric in object space. Stop Location: mm to the right / left of the first / second lens 13/18

14 b) (7 points) Determine the stop location reqired to make the sstem telecentric in image space. Stop Location: mm to the right / left of the first / second lens 14/18

15 5) ( 10 points) A thin lens in air is made of glass LAF7 (749348). The lens has a negative power, and it has a focal length of -100 mm. Determine the longitdinal chromatic aberration of this lens (δf). Sketch the relative locations of the F, d and C foci. Show δf. Longitdinal Chromatic Aberration = mm Inpt Ra 15/18

16 6) (Bons 5 points) If o are enrolled in the BS Optical Science and Engineering degree program, what track have o chosen (optics, electrical, mechanical or materials)? If o are in a different degree program, what is or major? 16/18

17 Spare ratrace forms: 17/18

18 Srface f φ t Srface f φ t 18/18

19 OPL = nl n sin θ = n sin θ γ= 2α n 1 d= t = t τ n φ= (n n)c OPTI-202R Eqation Sheet Final Exam 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 BFD = d + f R FFD = d + f F 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 10in 250mm MP = = f f 1 MP = m mv = mobjmpeye ω =ω φ n = n φ = +ωτ = + t 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)

20 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 nd 1 ν= n n n F n C d C P = n F n C ( α δmin ) sin ( α / 2) sin / 2 n = 1 n S θ C = sin nr δ = ( n 1) α δ ε = ν = P Δ Δ α 1 ν = δ ν ν nd1 1 α 1 ν = δ ν ν ε δ nd2 1 P P 1 2 = ν1 ν2 δφ δf 1 = = φ f ν TA CH rp = ν φ1 ν1 φ2 ν2 = = φ ν ν φ ν ν δφdc δfcd ΔP = = φ f Δν DOF = ± B f /# W L H fd LH = L B NEAR = 2

OPTI-502 Optical Design and Instrumentation I John E. Greivenkamp Homework Set 11 Fall, 2017

OPTI-502 Optical Design and Instrumentation I John E. Greivenkamp Homework Set 11 Fall, 2017 Assigned: 11/8/17 Lectre 23 De: 11/15/17 Lectre 25 11-1) A teleconverter is an optical component that is placed between or camera lens and camera to increase the focal length of the lens. Common varieties