Optical Engineering 421/521 Sample Questions for Midterm 1

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Alfred Beasley
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1 Optical Engineering 421/521 Sample Questions for Midterm 1 Short answer 1.) Sketch a pechan prism. Name a possible application of this prism., write the mirror matrix for this prism (or any other common prism) 2.) For the following system, create an error budget for the three lens elements. Consider only the stability of the element positions. Define a set of tolerances that limits image motion to 1 µm. You will need to estimate some parameters. The system has 10 mm entrance pupil diameter and 50 mm EFL. L1: 34 mm focal length L2: -17 mm focal length L3: 24 mm focal length 3.) In class, we developed a relationship that gives image position due to effect of a component using the beam footprint on the optics and the numerical aperture or focal ratio. Derive a similar relationship for an afocal system. 4.) What is the magic of the rhomboid, pentaprism, corner cube? 5.) Name 3 possible good merit functions for image quality of an average quality 35-mm camera lens. 6.) Consider an f/20 system with 500 nm light. Calculate the P-V wavefront error for 1 mm defocus. 7.) Calculate the rms wavefront error due to the 1 mm defocus above. 8.) Make a sketch that defines the mechanical and the optical axes of a lens 9.) A 25 mm diameter lens has a requirements of R = 100 +/= 0.1 mm. Calculate the tolerance in terms of the sag of the surface. Is this tight? 1

2 10.) For the two cases below, give the approximate shift in image position if the window is inserted into the converging beam as shown. Consider both axial and lateral effects. The window is 10 mm thick, n = 1.5, 50 mm from the image. The image is formed at f/10. Tilted at 45 Name the aberrations that would be caused by the plate for each case. 11.) Canon sells binoculars that actively stabilize the image using a variable wedge. The angular accelerations are measured with sensors and a correction is applied by changing the wedge of a fluid filled cavity. For the case of 10 x 35 binoculars, calculate the wedge required to fully the effect of tilting the binoculars by 1 mrad. a) Give the diameters of the entrance pupil and the exit pupil b) Give the value of the magnifying power c) If the binoculars are tilted by 1 mrad, how much motion does the user observe (hint: draw a sketch of this or you will probably get it wrong) d) Give the relationship between angular deviation at an element and system LOS for an afocal system e) Show the relationship between the wedge angle α and the deviation it causes in user space. f) Calculate the required wedge to correct for the 1 mrad tilt of the binoculars Object space α = wedge angle Variable wedge n = 1.8 User space unfolded prisms eyelens objective 25 mm beam footprint on wedge 12.) Draw a tunnel diagram for a dove prism. Give the mirror matrix. Draw ray paths for blue and red and use this to show why the dove prism does not suffer chromatic aberrations when used in collimated light 13.) Understand the definition of a datum on a drawing. Use ANSI Y14.5 convention to specify tolerances for straightness, flatness, roundness, profile, perpendicularity, parallelism, concentricity, position, and runout. 2

3 14.) Specify basic dimensions and tolerances using GD&T conventions 15.) Sketch a 3-view orthographic projection. Some possible parts: 3

4 16.) For the following system, determine the position of the nodal point and show it on the drawing. Show the position of the nodal point relative to point A: 20 mm aperture 0.1 NA 10 mm BFD 5 FOV Optical system A mm long ) What happens to the image if the lens above is rotated about point A by an angle of 1 mrad? 17.) Sketch a pentaprism. Give the mirror matrix. What is the magic of the penta prism? 18.) Sketch a rhomboid prism. Give the mirror matrix. What is the magic of this prism? 19.) Show the relationship between ETD and line of sight deviation for specifying wedge in a lens. 20.) A 25 mm diameter lens has a requirements of R = 500 +/= 1 mm. Calculate the tolerance in terms of the sag of the surface. Is this tight? 21.) Sketch a dove prism. Define three axes and write the mirror matrix for this prism. Draw its tunnel diagram. 22.) For the dove prism above, describe what happens if the prism is rotated by a small angle about each of the three axes. 41) Show how outside micrometers avoid the Abbe offset error that is present for calipers. 23.) Describe all of the tolerances as specified by the drawing below. (units are mm) 4

5 24.) Consider a 25 mm diameter, -250 mm focal length plano-concave lens was made with 25 µm ETD. Assume n = 1.5, so R = 125 mm (concave). Consider two cases, make a sketch for each: A) Assume the lens is mounted using the outer mechanical surface. Determine the angular deviation of light due to the wedge in the lens. B) If the lens is mounted such that the optical axis (defined by the two optical surfaces) is placed on the system axis, then the deviation will be zero. Determine the lens decenter (as defined by the outer edge) for such alignment.. 25.) A 20 mm diameter lens has a spherical surface with R = 200 mm. The tolerance for curvature allows 8 rings of power, (assume 0.5 um wavelength light). a) Determine the surface sag that corresponds to the 8 ring tolerance b) Determine the equivalent tolerance for the radius of curvature. 26.) Consider the following inverse telephoto lens, looking at an object far away Lens 1: 100 mm EFL f/4 focal ratio 60 field of view Lens 1: 90 mm diameter R1 = 100 mm R2 = 50 mm Ct = 5 mm N = 1.5 (-200 mm focal length) Assume that Lens 1 is manufactured with 1 mrad wedge. A) Determine the deviation of the light through the center of L1 due to its wedge 5

6 B) If L1 is mounted according to its mechanical axis, determine the shift in image position, relative to the case for a perfect lens. C) Determine the decenter of L1 required to achieve proper alignment 6. Sketch a 3-view orthographic projection of the following part, correctly showing all dimensions. (drawing in inches). Show how to specify the following: Surface A is parallel to B within 5 mrad (Hint: you need to convert this to a tolerance zone) B A 7.) What machine would be used to manufacture the part above (Problem 6) from aluminum? 8.) Use a sketch to show how outside micrometers avoid the Abbe offset error that is present for calipers. 6

Parity and Plane Mirrors. Invert Image flip about a horizontal line. Revert Image flip about a vertical line.

Parity and Plane Mirrors. Invert Image flip about a horizontal line. Revert Image flip about a vertical line. Optical Systems 37 Parity and Plane Mirrors In addition to bending or folding the light path, reflection from a plane mirror introduces a parity change in the image. Invert Image flip about a horizontal