Exam questions OPTI 517. Only a calculator and a single sheet of paper, 8 X11, with formulas will be allowed during the exam.

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1 Exam questions OPTI 517 Only a calculator an a single sheet of paper, 8 X11, with formulas will be allowe uring the exam. 1) A single optical spherical surface oes not contribute spherical aberration. Explain the situations when this can happen. 2) There is on wave of efocus at a wavelength of mm for a lens that is focusing light from an object point at infinity. The lens has a focal length of 100 mm an the aperture stop is at the lens an is 10 mm in iameter. Determine the longituinal change of focus. 3) Determine the raius of the Petzval surface in a lanscape lens (f=100 mm, n 1. 5 ). Explain how in the lanscape lens the effects of fiel curvature are mitigate. 4) Provie the fourth orer aspheric coefficient for the correcting plate of a Schmit camera where the primary mirror works at F/4 an the iameter is 200 mm. 5) A thin lens mae out of BK7 glass an with a focal length of 100 mm is working at F/10 an is place in an optical system. This lens oes not contribute chromatic aberrations. Explain where this lens is locate in the optical system. 6) A system of two thin optical weges in contact prouces a beam eviation D an contributes no primary spectrum (ispersion) an no seconary spectrum. Provie the wege angles (i.e. formulas) an glass characteristics for this system of weges. 7) Draw the wave fans, on axis an full fiel, for a system that has one wave of spherical aberration an minus one wave of fiel curvature. 8) Design a singlet lens at f/10 with a focal length of 100 mm that is free of coma an astigmatism. Provie the raii of curvature of the surfaces assuming the inex of refraction n 1. 5, an provie the stop location an iameter. The object is at infinity. Provie a neat rawing. 9) A iffractive optical element is esigne for λ=634 nm, for a focal length of f=100 mm, an an f number of 4. What is the optical power of the lens if it is use at a wavelength of 317 nm? Estimate the minimum zone with of this lens. What is the V number associate with this lens if the nominal wavelength at which it is use is λ 1 = 1200 nm, an the banwith limiting wavelengths are λ 3 = 1400 nm an λ 2 = 1000 nm. 10) Describe how a burie surface works an what it oes. 11) What are the o an even aberrations in the aberration function to fourth orer? 12) Write the monochromatic Seiel aberration coefficients for a single surface an etermine two conitions for the absence of spherical aberration coma an astigmatism.

2 13) Draw the wave fans, on axis an full fiel, for a system that has one wave of spherical aberration an minus one wave of fiel curvature. 14) A system has one wave of spherical aberration (one wave is mm). The image height is 0.03 mm for a fiel of view of one arc minute. Write the relationship between the wave aberration an the transverse ray aberration. Then etermine the transverse ray aberration for the marginal ray. Give your answer in millimeters. 15) Consier a concave parabolic mirror with a vertex raius of 1000 mm an a iameter of 200 mm. How much spherical aberration (as a wavefront eformation) oes it contribute when the object is at the center of curvature? 16) Consier a spherical mirror with a raius of 1000 mm. A an aspheric plate (n=1.5) to correct for spherical aberration when the object is at infinity. Where woul you place the aspherical plate so that the system is aplanatic? How much astigmatism the system has? What is the Petzval raius? Provie the fourth orer coefficient of asphericity for the plate surface. Sketch the system. 17) Describe how in the Schupmann meial telescope the chromatic change of focus W 020 an the chromatic change of magnification W 111 are correcte. Sketch the system an the chief an marginal rays. 18) Describe the four classical ways to correct fiel curvature an inclue neat rawings. 19) Design a singlet lens at f/10 with a focal length of 100 mm that is free of coma an astigmatism. Provie the raii of curvature of the surfaces assuming the inex of refraction n 1. 5, an provie the stop location an iameter. The object is at infinity. What is the image height for a semi fiel of view of 10 egrees? Provie a neat rawing. 20) A iffractive optical element is esigne for λ=634 nm, for a focal length of f=100 mm, an an f number of 4. What is the optical power of the lens if it is use at a wavelength of 317 nm? Estimate the minimum zone with of this lens. What is the V number associate with this lens if the nominal wavelength at which it is use is λ 1 = 1200 nm, an the banwith limiting wavelengths are λ 3 = 1400 nm an λ 2 = 1000 nm. 21) Write own the Coington equations an explain what entities they relate. Write own the Sine conition an explain what it means. Inclue rawings an mention any essential assumptions. 22) An f/10 optical system has 1 wave of efocus, what is the longituinal change in image location? Derive a relationship between the efocus wavefront eformation an the longituinal efocus. Assume the wavelength to be mm.

3 23) Describe how a burie surface works an what it oes. 24) Describe how the lens esign in the Brownie camera aresses: 1) spherical aberration, 2) coma, 3) astigmatism, 4) fiel curvature, 5) istortion, 6) chromatic change of focus an 7) chromatic change of magnification 25) Describe how the Petzval portrait lens esign aresses: 1) spherical aberration, 2) coma, 3) astigmatism, 4) fiel curvature, 5) istortion, 6) chromatic change of focus an 7) chromatic change of magnification 26) What is the ifference between real ray tracing an first orer ray tracing? 27) Write own the secon an fourth orer terms of the aberration function incluing the W coefficients an fiel an aperture epenence. There is a total of three secon orer terms an six fourth orer terms. Please inclue the aberration names. Do not inclue chromatic aberrations. 28) A f/10 system has 10 waves of focus. What is the image isplacement along the optical axis? One wave is mm. 29) An optical system has three waves of spherical aberration an one wave of coma at the ege of the fiel. Draw wave fan plots for the wavefront eformation on axis an at full fiel. 30) A concave spherical mirror is illuminate from a point object at infinity an its raius of curvature is 1000 mm. If the aperture iameter is 100 mm, how much spherical aberration is introuce by the mirror in the incoming light beam? 31) If the aperture stop is locate at the center of curvature of a spherical mirror, how much coma is present in the images prouce by this mirror? Make a rawing an explain why. 32) Mention three ways to correct for higher orer spherical aberration. 33) What is an aplanatic system? Mention one example. 34) A thin lens has a focal length of 100 mm an is mae out of BK7 glass (n=1.51, v=64). The stop is contact with the lens. If the lens works at f/10 how much longituinal an transverse chromatic aberrations are generate? 35) For a system of two weges in contact, what is the conition to avoi light ispersion? Write own the relevant equation. Explain. 36) Write own the Seiel sum formulas for spherical aberration an coma. 37) Write own the surface contributions to the fourth orer wave aberrations incluing the chromatic aberrations.

4 38) A plano convex lens mae out of BK7 glass (n=1.517 an V=64.2) is working at f/10. The aperture stop coincies with lens an is 100 mm in iameter. The full fiel of view is 1 egree. What is the size of the image? Calculate the chromatic change of focus an the chromatic change of magnification. 39) An optical system has 2.0 waves of fiel curvature an 2.0 waves of spherical aberration. Draw the on axis an full fiel OPD plots (tangential an sagittal fans). 40) A plano convex lens mae out of glass with n=1.5 an with thickness of 10 mm. The raius of curvature of the convex surface is 100 mm. The object is at infinity. Where shoul be the stop locate so that no coma or astigmatism are introuce by the lens? 41) The mirror of a Schmit camera works at f/2 an the focal length is 250 mm. How much spherical aberration oes this mirror contribute? What is the coma contribute by the mirror at 1 egree fiel of view? 42) Explain two examples about how a fiel lens helps to correct aberrations. 43) A fiel lens is mae out of BK7 glass an has a focal length of 25 mm. How much spherical aberration an coma oes it contribute? What is its contribution to the Petzval sum? 44) Briefly state the sine conition. Write the equation an efine the parameters involve. 45) Which type of Cassegrain like telescope is aplanatic? 46) List three calculations one in a lens esign program that use paraxial ray tracing an list three calculations using real ray tracing. What is the ifference between paraxial an real ray tracing? 47) Explain how a Wollaston meniscus lens works. Make a sketch showing the meniscus, the stop, the image plane, an the marginal an chief rays. Explain how the seven aberrations are controlle in this lens. 48) Provie an equation an a graph about the variation of spherical aberration with the lens shape factor. Explain how spherical aberration is correcte in the Maksutov camera. 49) There is one wave of efocus at a wavelength of mm for a lens that is focusing light from an object point at infinity. The lens has a focal length of 100 mm an the aperture stop is at the lens an is 10 mm in iameter. Determine the longituinal change of focus ue to the efocus an provie a graph of the wavefront eformation at the exit pupil.

5 50) Determine the raius of the Petzval surface in a lanscape lens (f=100 mm, n 1. 5 ). Explain how in the Wollaston lanscape lens the effects of fiel curvature are mitigate. Describe two methos to control fiel curvature. 51) Provie the fourth orer aspheric coefficient for the correcting plate of a Schmit camera where the camera primary mirror works at F/4 an the iameter is 200 mm. 52) A thin lens mae out of BK7 glass an with a focal length of 100 mm is working at F/10 an is place in an optical system. This lens oes not contribute chromatic aberrations. Explain where this lens is locate in the optical system. 53) A system of two thin optical weges in contact prouces a beam eviation D=5 egrees an contributes no primary spectrum (ispersion). If the glasses are an provie the wege angle for both weges. 54) Draw the wave fans, on axis an full fiel, for a system that has one wave of spherical aberration an minus one wave of coma aberration. 55) Design a singlet lens at f/10 with a focal length of 100 mm that is free of coma an astigmatism. Provie the raii of curvature of the surfaces assuming the inex of refraction n 1. 5, an provie the stop location an iameter. The object is at infinity. Provie a neat rawing. 56) In the glass P V iagram escribe how you chose the glasses for a two lens apochromatic objective an for a three lens apochromatic objective. 57) Describe how a burie surface works an what it oes. Theoretically, how chromatic aberrations W 111 an W 020 are correcte in the Maksutov camera? 58) A lens system working in air an at F/5 has 2 waves of coma aberration where a wavelength is mm. Make a plot of the saggital an tangential wave fans at full fiel. Determine the transverse ray aberration for 1 at full fiel. If spherical aberration an coma aberration are correcte, how such a system is often calle? 59) Design a relay lens with a magnification of 1 that is correcte for spherical aberration, coma an astigmatism. No more than three elements are allowe an only one aspheric surface is permitte. The system must have positive optical power. Sketch carefully an in etail your esign. Explain how the aberrations are correcte an provie the shape, optical power, an positions of the elements an the position of the stop ) Use the formula RS exp to etermine what shoul be to have a Raleigh Strehl ratio of 0.8. Explain what this formula refers to.

6 61) A singlet thin lens with a focal length of 100 mm is use to image the Moon. The stop aperture is at the lens which works at F/10. Determine the amount of istortion aberration. Determine the amount of astigmatism aberration. 62) Provie the fourth orer aspheric coefficient for the correcting plate of a Schmit camera where the camera primary mirror works at F/4 an the iameter is 200 mm. 63) A thin lens mae out of BK7 glass an with a focal length of 100 mm is working at F/10 an is place in an optical system. This lens oes not contribute chromatic aberrations. Explain where this lens is locate in the optical system. 64) A iffractive optical element works at F/10 at a wavelength of mm. Determine what is the longituinal epth of focus for 1 wave of efocus. Determine what the minimum zone spacing is. Determine what the longituinal chromatic focal shift is for the F an C wavelengths. 65) Describe how each of the primary aberrations an chromatic aberrations are controlle in the Wollaston meniscus lens. Make a sketch of the lens incluing the aperture stop, chief an marginal rays. Arrange your answer in a list of seven bullet items one for each aberration. 66) A plano convex lens mae out of Bk7 glass (517642) is working at f/10. The aperture stop coincies with lens an is 100 mm in iameter. The full fiel of view is 1 egree. What is the size of the image? Calculate the longituinal chromatic aberration as a longituinal quantity an the lateral chromatic aberration. 67) Write own the surface contributions to the fourth orer wave aberrations incluing the chromatic aberrations. 68) An optical system has 1 wave of coma an 5 waves of spherical aberration. Draw the onaxis an full fiel OPD plots (tangential an sagittal fans). 69) A plano convex lens mae out of glass with n=1.5 an with thickness of 10 mm. The raius of curvature of the convex surface is 100 mm. The object is at infinity. Where shoul be the stop locate so that no coma or astigmatism are introuce by the lens? 70) The mirror of a Schmit camera works at f/4 an the focal length is 500 mm. The stop is at the center of curvature. How much spherical aberration oes this mirror contribute? What is the coma contribute by the mirror at 1 egree fiel of view? 71) Explain two examples about how a fiel lens helps to correct aberrations.

7 72) A fiel lens is mae out of BK7 glass an has a focal length of 25 mm. How much spherical aberration an coma oes it contribute? What is its contribution to the Petzval sum? 73) Briefly state the sine conition. Write the equation an efine the parameters involve. 74) What is the raius of curvature of the sagittal surface for a spherical mirror of raius R when the object is at infinite? The stop is locate at the mirror. You can use the Coington equations to answer this question. 75) Explain how an Offner null corrector works. Make a sketch showing the null corrector in relation to the mirror uner test. What is the function of lenses in the null corrector? 76) How o I choose the glass types to make the seconary spectrum zero in a oublet? 77) Explain how the aplanatic concentric lens works.

1.0 MEASUREMENT OF PARAXIAL PROPERTIES OF OPTICAL SYSTEMS

1.0 MEASUREMENT OF PARAXIAL PROPERTIES OF OPTICAL SYSTEMS .0 MEASUREMENT OF PARAXIAL PROPERTIES OF OPTICAL SYSTEMS James C. Wyant Optical Sciences Center University of Arizona Tucson, AZ 8572 jcwyant@u.arizona.eu If we wish to completely characterize the paraxial