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

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1 Assigned: 11/8/17 Lectre 23 De: 11/15/17 Lectre ) 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 are 2X and 3X teleconverters. A 2X converter sed with a 135 mm lens will reslt in an effective sstem focal length of 270 mm. A teleconverter consists of a fixed grop of elements (consider it to be an eqivalent singlet) in a tbe of fixed length. It has no moving components and will work with an camera lens. In addition to its focal length, the other two parameters o need to know abot the teleconverter are the tbe length D and the position of the singlet from the detector plane L. Both of these are fixed and independent of the camera lens sed. Camera Lens Teleconverter L D Detector a) Determine the focal length of an N-X teleconverter. Assme that the object is at infinit. Provide the necessar eqations to show that the sstem focal length is increased b N and the image is still in the film plane. Show that D and L are related. b) What happens to the f/# of the sstem with a teleconverter? c) Provide a tpical design for a 3X converter with D = 50 mm.

2 11-2) Design three different eepieces for an optical sstem. All three eepieces have a Magnifing Power of 10, and are to be sed with a relaxed ee (the image presented to the ee is at infinit). The sstem objective presents an intermediate image to the eepiece, and the intermediate ppil of the sstem is 200 mm to the left of this intermediate image plane. This intermediate ppil is the image of the stop throgh an optical elements between the stop and the eepiece. a) A simple eepiece consisting of jst an ee lens. Determine the focal length and the ee relief. b) A compond eepiece with a field lens located at the intermediate image plane. The field lens has a focal length of 40 mm. Determine the ee relief. c) A Ramsden-stle eepiece with the same ee relief as fond with compond eepiece of part (b). The field lens is located 12 mm to the right of the intermediate image plane. Determine the focal lengths of the two lenses and their separation. Hint: Three conditions mst be met b the design -- the eepiece mst have the proper magnifing power, the final image presented to the ee mst be at infinit, and the reqired ee relief mst be obtained. 11-3) Eeglasses are sed when the focs of the ee does not fall on the retina. With mopia (nearsightedness), ras from a distant object focs in front of the retina. With hperopia (farsightedness), these ras focs behind the retina. For the prposes of this problem, the ee can be modeled as a spherical refracting srface of index n. a) Eeglasses are sall placed near the front focal point of the ee (assme the are at F). If G is the power of the eeglasses and E is the power of the ee, what is the sstem power? b) Based on this answer, how do eeglasses work? c) What happens if the eeglasses are not at the front focal point of the ee? d) What is the sign of the power reqired to correct mopia and hperopia? e) As a comparison, how do contact lenses work?

3 11-4) The goal of this problem is to design a door peephole to view or visitors (o see them, bt the don t see o). The ee shold be inclded as part of the design, and for this problem we will model the ee as a single refracting srface of radis 5.65 mm. The index of the ee is that of water (1.333), and the ppil or iris diameter is 4 mm and is located at the cornea. The retina is located at the rear focal point of the cornea. The macla is the central portion of the retina and is specialized for resoltion. The fovea is the highest resoltion part of the macla and has a diameter of abot 1.5 mm. The resoltion of the retina drops off otside the macla. The macla has a diameter of abot 3 mm, and we will somewhat arbitraril se an area of abot 1.5 times the macla diameter to define the visal field of view for this application. The peephole is a non-inverting afocal sstem sed to increase the field of view of the ee throgh the door. The iris of the ee is the sstem stop. a) Design a thin-lens peephole that covers a total field of 90 and has a total length of 25 mm (it has to fit within the thickness of the door). b) What are the reqired element diameters for a totall vignetted field of this size? The separation between the cornea and the rear element of the optical sstem shold also be 25 mm (nose room). c) Given that the illminance prodced b a fll moon on the earth s srface is 0.27 lm/m2, what is the illminance prodced on the retina sing this sstem? Remember that the image at the retina is in water. 11-5) A 10X Keplerian telescope is constrcted ot of a 200 mm focal length objective lens and a 20 mm focal length ee lens. The sstem stop is at the objective. a) What are the length (from objective lens to ee lens) and ee relief of this telescope? b) Add a rela lens to the telescope to correct the image orientation and to increase the magnifing power of the telescope to 20X. The focal length of this lens is 30 mm. What are the element separations, the sstem length and the ee relief? c) Now add a field lens at the first intermediate image plane of the telescope to image the objective lens (stop) of the sstem into the rela lens apertre. The overall sstem length does not change. Determine the focal length of this field lens and the ee relief. d) If the sstem has a field of view of +/- 1 degree, what are the reqired diameters of the field lens and the rela lens? The objective diameter is 20 mm.

4 11-6) A Cassegrain Objective consists of a concave primar mirror and a convex secondar mirror. The sstem stop is located at the primar mirror. The working distance is defined from the vertex of the primar mirror to the image plane. For the prposes of this problem, assme that the mirrors have zero thickness. The object is at infinit. The maximm image size is +/- 8 mm. The sstem operates at an f- mber of f/4. The sstem specification is (onl the magnitdes of the qantities are provided): R P = 500 mm R S = 125 mm t = 200 mm R S D H R P Image Plane (+/- 8 mm) z t WD Determine the following: - Sstem focal length and the working distance. - Diameter of the Primar Mirror D P - The location and diameter of the Exit Ppil - The reqired diameter of the Secondar Mirror D S and reqired diameter of the Hole in the Primar Mirror D H the sstem to be nvignetted over the specified Image Size. - The anglar Field of View of the sstem in Object Space NOTE: This problem is to be worked sing ratrace methods onl. All answers mst be determined directl from the ras o trace; for example, the FOV mst be determined from the chief ra. Ratraces mst be done on the ratrace form. Be sre to clearl label or ras on the ratrace form. A method of soltion explaining or procedre and calclations mst be provided. Gassian imaging methods ma not be sed for an portion of this problem.

5 11-7) The prchasing department made a large mistake and ordered several hndred thosand 50 mm focal length lenses for a now-cancelled program. Faced with the dilemma of what to do with all these non-retrnable lenses (and sensing an opportnit to single-handedl save the compan), or boss walks into or office and proclaims Riflescopes the ftre is riflescopes! Section A Yor boss now orders o to design a 3X25 riflescope sing onl these 50 mm focal length thin lenses. Yor boss also insists that o onl se three of these lenses per riflescope. A riflescope is a relaed Keplerian telescope (afocal with an erect image). The stop is at the objective lens, and the object can be considered to be at infinit. For this three-element sstem, determine the element spacings, locations of an intermediate image planes (for crosshairs), the overall sstem length, the ee relief and the XP diameter. Section B The object space FOV of the riflescope is 3 degrees (HFOV is 1.5 degrees). Determine the reqired element diameters for this three-element sstem to be nvignetted over this FOV. Provide a sstem laot showing the marginal ra. (At this point in the design process, o do not know the available element diameters.) Section C Yor boss reviews or three-lens design and sas That s nice, bt all the lenses we have are onl 25 mm in diameter. What are the implications of this limitation to or design? Can o provide a 3X25 design sing jst three of these lenses? Section D Confident in or abilities, or boss now demands that o design a 4X25 riflescope with an overall length of exactl 300 mm (objective to ee lens). As a single concession, o are now permitted to se for of the 50 mm focal length thin lenses. The stop is at the objective, and the fll nvignetted FOV remains at 3 degrees. The design approach is to replace the rela lens with an air-spaced pair of lenses. As before, provide the element spacings, locations of an intermediate image planes (for crosshairs), the overall sstem length, the ee relief, the XP diameter, and the reqired element diameters. Provide a sstem laot showing the marginal ra. Does this for-element sstem assembled ot of existing eqal lenses look like a reasonable design for a riflescope? Note: This is a first-order design problem. All lenses can be assmed to be thin lenses with no

6 aberrations and no thickness. To aid in grading, this problem ma be more completel specified than o wold normall enconter. In fact, the approach specified ma or ma not be the best form of the soltion. All of the given specifications mst be met exactl. IMPORTANT -- The problem is to be worked in sections. Each section mst start on a new page of or soltion. In addition, a smmar page with a diagram of the sstem is attached where all of the pertinent details of or design mst be shown. This smmar page is to be sed as the cover page of or soltion.

7 NAME Cover Sheet for Soltion Section A and B (also show intermediate image planes) Objective/Stop 25 mm Rela Ee Lens XP Section C Smmar comments Section D (also show intermediate image planes) Objective/Stop 25 mm Rela 1 Rela 2 Ee Lens XP 300 mm

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9 Srface C t n t/n