ECEN 4606, UNDERGRADUATE OPTICS LAB

ECEN 4606, UNDERGRADUATE OPTICS LAB Lab 2: Imaging 1 the Telescope Original Version: Prof. McLeod SUMMARY: In this lab you will become familiar with the use of one or more lenses to create images of distant objects. You will quantify the performance of these instruments via measures such as their magnification and field of view. The goal of the lab is to discover how the different specifications of the optical system (the focal lengths and diameters of the lenses) impact its operation. In this lab, your eyes and a CMOS camera will be the detectors. GLOSSARY: OBJECT: The source of the optical intensity. What is being viewed. The input. IMAGE: An imperfect copy of the field emitted by the object. Generally the output, although images can also occur at intermediate planes. OBJECTIVE: The first optical element of a telescope which can be either a lens or a curved mirror. Its function is to transform the nearly parallel rays from the distant object to an intermediate image that is located very near to the back focal plane of the objective. The objective is almost always the aperture stop. EYEPIECE: The second optical element of a telescope which is nearly always a compound (multi-element) lens. Its function is to magnify the real, intermediate image produce by the objective. If the image receiver is a camera, the eyepiece must produce a real image. If the telescope is designed to be looked through (the image receiver is a human eye), the eyepiece will typically be adjusted to produce a virtual image. Usually, this is the field stop. APERTURE STOP: The optical element (typically a lens edge or iris diaphragm) which limits the cone of rays accepted from the center (on axis) portion of the object. The sine of the largest angle in this cone is the numerical aperture in object space. The aperture stop controls how much light is accepted and the resolution of the telescope, thus you typically want it to be as large as your size and cost budget will allow. FIELD STOP: The optical element (typically a lens edge or iris diaphragm) which limits the area of the object that can be seen. The black circle surrounding the image, visible in binoculars or a microscope, is an image of the field stop. VIGNETTING: The loss of rays in an optical system causing decreased power and resolution. Vignetting is most common near the edge of the field, appearing as a darkened boundary. RESOLUTION: The spatial impulse response of the system. It can be measured as a size (e.g. the radius of the diffraction pattern) or a cutoff spatial frequency. Resolution is ideally limited only by diffraction, but aberrations, receiver pixels size and other effects can increase the resolvable spot size. Resolution can be measured in object or image space these will be related by the magnification of the system. Version 1.3, 8/15/12 McLeod and Gopinath 1

ABERRATION: Imperfections in the performance of the system that cause the image be an imperfect version of the object. Examples include astigmatism and distortion. PRELAB: The three designs below correspond to the three primary steps of the lab. There are also several homework style problems to increase your understanding. DESIGN PROBLEM 1: Design a single-lens optical imaging system that has magnification M = -1. This system (object, lens, and image) should fit entirely on the rail, listed below. DESIGN PROBLEM 2: Design a single-lens optical imaging system that has magnification M = -1/10. This system (object, lens, image) will not fit entirely on the rail, but should fit on the optics table. Use the same lens you used for problem 1 so that you can easily shift between these systems and also so you can compare their performance. DESIGN PROBLEM 3: Design a single-lens eyepiece to follow the objective of problem 2 that will provide M = -5 magnification between the intermediate image plane and the final image plane. This two-lens telescope, measured from the objective lens to the final image plane, should fit entirely on the rail. HOMEWORK PROBLEM 1: Problem 3-26. Note that the answer is in the back of the book. HOMEWORK PROBLEM 2: Consider the objective of an astronomical telescope with objects ~at infinity which therefore forms an image ~in the focal plane of the objective. Let the focal length (F), diameter (d) and optical wavelength (λ) be specified. Since the objects are an unknown distance away, typically, we can t use object size, so instead will use object angle α away from the optical axis. Version 1.3, 8/15/12 McLeod and Gopinath 2

Trace a single ray through the center of the objective to the intermediate image plane and use this to write a formula for the translation of angular coordinate in the object space to physical height of the image in the intermediate image plane. Remember we are using the paraxial (small angle) approximation here, so you can simplify any trig functions to their lowest Taylor-series term. If two stars just resolvable in the telescope in that they land just in the nulls of each other s impulse response, what is their angular separation? Remember, from lecture #2, that: Calculate this angular resolution for the Hubble space telescope with objective focal length of 1.5 m, objective diameter of 2.4 m, and operating in the green at 500 nm wavelength. Imagine we used this same objective (focal length and diameter are unchanged) as a radio telescope observing 1 MHz radio waves how is the angular resolution changed? This is why radio telescopes are REALLY LARGE. TECHNICAL RESOURCES: r spot = 1.22λ 0 TEXTBOOK: Chapters 2 and 3 LECTURE NOTES: Lecture 2, the Telescope. ( F D) EQUIPMENT AVAILABLE: 24 long optical rail and lens rail carriers for easy linear alignment of objective and eyepiece. A lamp with a fiber-bundle for illumination of your object. A diffuser (a non-glare page protector) to place behind your objects in order to spread the illumination from the fiber- bundle more evenly. Transparent and opaque grids of various scales to use as objects and to place on image screens for comparison. One square of the grid is filled (black) to determine orientation of the image relative to the object. White screens for use as image planes. Lenses: focal lengths of 50, 100 and 250 mm Objective lens Aperture stop Field stop Eyepiece Screen Figure 1. Layout of telescope at the completion of step 3. Version 1.3, 8/15/12 McLeod and Gopinath 3

LAB PROCEDURE: STEP 1: 1:1 IMAGING WITH A SINGLE LENS Select a transparency to use as an object and tape it to the front of the cardboard screen with the hole. Tape the diffuser to the opposite side. Place the fiber bundle at least one foot behind the transparent target so that the light has sufficient distance to diffract and fill the transparency. Set up the unity magnification system you designed in prelab problem 1 on the optical rail. The rail will allow you to easily move elements just along the optical axis. First make sure the object plane, the lens and the image plane are all perpendicular to the rail by looking down on the rail and rotating the parts in the post holder, then tightening the set screws. Second, adjust the object-lens and lens-image distance to meet two conditions: unity magnification (determined by the identical object and image grids overlapping) and good focus (determined by the sharpest possible image). Are the two adjustments independent or coupled? Optimize the image (for both conditions) at the center of the field. Remember to lightly tighten the set screws that hold the rail carriers in place once you have an optic positioned correctly. In your lab book: When you are finished, measure the distances and compare to your design. Note that the location of the lens is not a single plane, making distance measurements slightly ambiguous this problem is solved with the concept of principal planes. Do the two grids perfectly overlap everywhere or is there some deviation at the edges of the field? This is the effect of distortion which is one of the classical aberrations. Fish eye lenses are an example of a highly distorted system. Using the darkened square on the grid, comment on the sign of the magnification. Does this agree with your expectation via ray-tracing? Remove the grid from the image plane and examine the sharpness of the lines at the center of the field and the edges. Defocus and other blur at the edges of the field are due to other aberrations (field curvature, coma, astigmatism). Finally, loosen the set screw in the object post-holder and rotate the object slightly. The image will become defocused on the edges, so rotate the image plane in the same way. Hint: If you extend a line from the object and image planes, these lines should intersect in the lens plane. You should be able to return to a condition of reasonably good focus, but the grid on the image plane will now look different. Can you explain your observation? STEP 2: IMAGING A DISTANT OBJECT WITH A SINGLE LENS (THE OBJECTIVE) Change the object and image locations to create a M=-1/10 system as designed in prelab problem 2. Shift your objective to the front of the rail (near to the object) so that you will have room to set up the eyepiece on the back end of the rail in step 3. Use the 1/10 scale grid on the image plane and align the system as you did in step 1. The object is not on the rail, so be careful to position all of the elements on the optical axis and perpendicular to it. Version 1.3, 8/15/12 McLeod and Gopinath 4

If your image is of low contrast, you may have to block scattered light from the object which is missing the lens. If you see a uniform, small bright spot in the image, you are seeing the image of the fiber bundle and your diffuser is not sufficient move the source back or add additional diffusers. In your lab book: Measure your distances and again compare to your design. Compare this system to the first using the techniques above (don t tilt the object in this case). If the illumination of the object is approximately the same, what do you notice about the brightness of the image in comparison to your first system? Why? Place an iris immediately after the objective lens, centered on the lens. This is the aperture stop of the system. As you reduce the diameter of this stop, what do you observe about the brightness, resolution and visible field (area of the grid you can see) at the intermediate image plane? Now, you will replace the screen with a CMOS camera that is connected to the computer. We need to first calibrate the camera. Arrange the lamp to illuminate a transparency with known gridlines in front of the camera. Use the corresponding image obtained on the computer to perform a calibration (1 pixel =? inches or? cm). Then, place the camera where the screen in your imaging setup with M = -1/10 original was placed. Capture the image, and determine the size. Is your imaging system operating with the correct magnification? STEP 3: USING A SECOND LENS TO INCREASE MAGNIFICATION (THE EYEPIECE) Temporarily use the back of the intermediate image screen as a new object and set up your eyepiece as designed in prelab problem 3 on the back end of the rail. Use the 1/2 scale grid (M Total = M Obj M EP = (-1/10)(-5) = ½), as before, to achieve the design magnification and focus. Remove the intermediate screen from the post-holder at the intermediate image plane and insert an iris at this plane, centered on the image. This is your field stop. Note that many telescopes, including that drawn in the notes, do not include this iris and instead use the eyepiece as the field stop this particular location is better however because the image is in-focus here. In your lab book: Fully open both the aperture stop and the field stop and compare this system to the previous one without the eyepiece. Reduce either the aperture stop or the field stop and observe the impact on the final image. STEP 4 IF YOU HAVE TIME: REAL VS VIRTUAL IMAGES Remove the screen from the final image plane and try to look at the image with your eye. Describe your eye location and the image quality. Then, loosen the rail-carrier screw on the eyepiece lens and move the lens towards the intermediate image plane, adjusting your eye location to maintain the best image. Note the distance between the field stop at the intermediate image plane and the eyepiece lens it is likely equal to or just less than the eyepiece focal length. Version 1.3, 8/15/12 McLeod and Gopinath 5

In your lab book: If the distance between the intermediate image and the eyepiece lens is less than or equal to the focal length of the eyepiece, the telescope cannot form a final, real image, so how are you seeing this? For sake of analysis, assume that the intermediate image plane to eyepiece focal distance is exactly the eyepiece focal length and use graphical ray tracing to analyze the three lens system of object-objective lensintermediate image plane-eyepiece lens-cornea-retina. Let the object be ~infinitely far away so that incident rays from object points are parallel (as done in the notes). The intermediate image plane is one objective focal length behind the objective. Treat the cornea as a 25 mm lens. This is a relatively real optical design (in the paraxial limit) congratulations! Version 1.3, 8/15/12 McLeod and Gopinath 6

Name Name and group members. Abstract (10 points). Introduction (10 points) Grading Expectations Lab Report 2: Imaging 1 (100 total points) Methods (35 points) Single lens imaging (11 points - 5 for figure, 5 for description). Imaging with distant object, M = -1/10 system (12 points, 6 - for description, 6 for figure). Second lens to increase magnification (7 points, 3 for description, 4 for figure) Real vs. Virtual images (5 points, 3 for description, 2 for figure) Results and Analysis (35 points) Single lens imaging(10 points, 4 points for discussion of image quality,3 points for magnification, 3 points for rotation of object and discussion of result) Imaging with distant object, M = -1/10 system (12 points,4 for distance measurements/brightness of image compared with single lens, 4 for aperture stop, 4 for calibration of camera and verification of -1/10 imaging) Second lens to increase magnification (7 points - description of effect of aperture and field stop) Real vs. virtual images (6 points - 3 points for ray tracing diagrams below, and 3 points for explanation). e. Conclusion (10 points) f. References Version 1.3, 8/15/12 McLeod and Gopinath 7