Difference between revisions of "Optics Bootcamp"

Overview

You are going to build a microscope next week. The goal of the Optics Bootcamp exercise is to make that seem like a less intimidating task.

The Bootcamp starts with a few ray optics problems. After you do the problems, you will build an imaging apparatus made from some of the same optical components you will use in the microscopy lab. The apparatus includes an LED illuminator, an object with precisely spaced markings, a lens, and a CCD camera. You will compare measurements you make in lab of the object distance, image distance, and magnification to the values predicted by the lens makers' formula that was covered in class. Do the problems ahead of time or come in to the lab if you would like some help. Then go ahead do the lab work.

And let's be careful out there. (This is a reference to a TV series that originally aired probably about a decade before you were born.)

Problems

Snell's law

A laser beam shines on to a rectangular piece of glass with thickness T at an angle $ \theta $ of 45° from the surface normal, as shown in the diagram. The index of refraction of the glass, ng, is 1.41 ≈√2. The index of refraction for air is 1.00.
(a) At what angle does the beam emerge from the back of the glass?
(b) When the beam emerges, in what direction (up or down) and by how much will it be displaced from its original axis of propagation?

Chelonian size estimation

In the diagram above, an observer at height S above the surface of the water looks straight down at a turtle swimming in a pool. The turtle has length L, height H, and swims at depth D.
(a) Use ray tracing to locate the image of the turtle. Show your work.
(b) Is the image real or virtual?
(c) Is the image of the turtle deeper, shallower, or the same depth as its true depth, D?
(d) Is the image of the turtle longer, shorter, or the same length as its true length, L?
(e) Is the image of the turtle taller, squatter, or the same height as its true height, H?

Ray tracing with lenses

Lenses L1 and L2 have focal lengths of f1 = 1 cm and f2 = 2 cm. The distance between the two lenses is 7 cm. Assume that the lenses are thin. The diagram is drawn to scale. (The gridlines are spaced at 0.5 cm.) Note: You might want to print out this diagram so you can trace the rays directly onto it.

(a) Use ray tracing to determine the location of the image. Indicate the location on the diagram. How far to the right of lens L2 is the image located?
(b) Is the image upright or inverted? Is the image real or virtual? Explain.
(c) What is the magnification of this system?
(d) Lens L1 is made of BK7 glass with a refractive index n1 of 1.5. Lens L2 is made of fluorite glass with a refractive index n2 of 1.4. Compute the focal lengths of L1 and L2 if they are submerged in microscope oil (refractive index no = 1.5).

Gather materials

Imaging apparatus with illuminator, object, lens, and CCD camera mounted on an optical rail.

Before you get started, take a little time to learn your way around the lab. This page gives an overview of all the wonderful resources in the lab.

Parts for the simple imaging apparatus.

The first step is to gather the materials required to build the lens measuring apparatus. The lists below include part numbers and descriptive names of all the components in the apparatus. It is likely that you will find some of the terms not-all-that-self-explanatory. Most of the parts are manufactured by a company called ThorLabs. If you have a question about any of the components, the ThorLabs website can be very helpful. For example, if the procedure calls for an SPW602 spanner wrench and you have no idea what such a thing might look like, try googling the term: "thorlabs SPW602". You will find your virtual self just a click or two away from a handsome photo and detailed specifications.

Optomechanics

These components are located in plastic bins on top of the center parts cabinet:

• 1 x RLA1800 dovetail optical rails
• 4 x RC1 rail carriers
• 1 x SM1L10 lens tube
• 1 x SM1RC lens tube slip ring
• 1 x CP02 cage plate
• 1 x LCP01 cage plate (looks like an "O" in a square)
• 1 x LCP02 cage plate adapter (looks like an "X")
• 2 x SM2RR retaining rings

These components are located on the counter above the west drawers.

• 4 x ER1 cage assembly rod (The last digit of the part number is the length in inches. Take a 1" rod. Lengths less than 1" have a part number that starts with a zero.)
• 6 x SM1RR retaining rings

Screws and posts

Stainless steel, ¼-20 size, socket head cap screws (SHCS), washers, posts, and post holders are located on top of the west parts cabinet. If you are unfamiliar with screw types, take a look at the main screw page on the McMaster-Carr website. Notice on the left side of the page that there are about ... links on the left side of the page. Click the links for more information about screw sizes and attributes. This link will take you to an awesome chart of SHCS sizes.

• 4 x PH2 post holders
• 4 x TR2 optical posts
• 4 x 8-32 set screws
• 6 x 1/4-20 x 5/16" socket cap screws
• 1 x 1/4-20 set screw

Optics

Lenses and microscope objectives are located in the west drawers.

• 1 x LA1951 plano-convex, f = 25 mm lens
• 1 x LB1811 biconvex, f = 35 mm lens

Object

Imaging targets are located in a plastic bin on top of the east cabinet.

• 1 x R1DS1N 1951 USAF test target

Optoelectronics

LEDs will be in a plastic bin on top of the center cabinet.

• 1 x red, super-bright LED (mounted)

Tools

Most of the tools are located in the drawers at your lab station. Be sure to put all of the tools you use back in their proper location.

Hex keys (also called Allen wrenches) are used to operate SHCSs. Some hex keys have a flat end and others have a ball on the end, called balldrivers. The ball makes it possible to use the driver at an angle to the screw axis, which is very useful in tight spaces. You can get things tighter (and tight things looser) with a flat driver.

• 1 x 3/16 hex balldriver for 1/4-20 cap screws
• 1 x 9/64 hex balldriver
• 1 x 0.050" hex balldriver for 4-40 set screws (tiny)
• 1 x SPW602 spanner wrench

You will also need to use an adjustable spanner wrench. The adjustable spanner resides at the lens cleaning station. There is only one of these in the lab. It is likely that one of your classmates neglected to return it to the proper place. This situation can frequently be remedied by yelling, "who has the adjustable spanner wrench?" at the top of your lungs. Try not to use any expletives. And please return the adjustable spanner wrench to the lens cleaning station when you are done.

• 1 x SPW801 adjustable spanner wrench

Things that should already be (and stay at) your lab station

• 1 x Manta CCD camera
• 1 x Calrad 45-601 power adapter for CCD
• 1 x ethernet cable connected to the lab station computer

Build the apparatus

		Optical rails Optical rails are useful for arranging components in a line that require variable separation. Sliding clamps sit on the rail. The clamps have a thumbscrew that locks them in position. Secure the optical rail on the optical table using two 1/4-20 x 5/16 cap screws and the 3/16 hex balldriver. Prepare four sliding posts, each by attaching one RC1 rail carrier to one PH2-ST post holder with one 1/4-20 x 5/16 cap screws.
		Mount the LED light source: In the LCP01 cage plate, the LED will get sandwiched in-between two SM2RR retaining rings. First screw in one SM2RR only 1 mm deep. Next place the LED above it. Finally tighten down the second SM2RR using the SPW801 adjustable spanner wrench. The SPW801 can be opened until its width matches the SM2RR diameter, the separation between the ring's notches. In the LCP02 cage plate adapter, screw in on SM1RR 3 mm deep. Carefully (use lens paper unsparingly to protect the lens surface) place the 25 mm plano-convex lens above it, with the hemisphere facing down yet not touching any potentially damaging surface. Tighten down a second SM1RR using the SPW602 spanner wrench, whose guide flanges sit in the ring's notches to prevent any scratching of the lens's optical surface. Attach the LCP01 cage plate (holding the LED) to the LCP02 adapter (holding the 25 mm condenser lens), using the 0.050" hex balldriver to secure four ER1 rods with eight 4-40 set screws. Affix a TR2 optical post to the LCP01 cage plate (holding the LED). Slide in the LED assembly along the optical rail. Power the LED light source: The red LED will be connected to a DC power supply. Ensure that the current limit on the power supply (CH1) is set to a value below 0.5 A. Connect channel CH1 to the red and black threads of the LED, using alligator clip cables. Turn on the power supply, and press its Output button to light the LED. Adjust the LED brightness using the power supply's Voltage knob.
	Mount the object (US Air Force target 1951): Tighten the R1DS1N 1951 USAF test target in-between two SM1RR retaining rings inside the SM1L10 lens tube, using the SPW602 spanner wrench. (This procedure should be reminiscent of the insertion of the 25 mm hemispherical lens in the cage plate adapter.) Slide in the lens tube through the SM1RC slip ring. By rotating the lens tube, you will be able to modify orientation of the object. Lock the lens tube in place using the 9/64 hex balldriver. Affix a TR2 optical post to the SM1RC slip ring (holding the USAF target). Slide in the object assembly along the optical rail. Mount the lens (f = 35 mm): Tighten the LB1811 biconvex f = 35 mm lens in-between two SM1RR retaining rings inside the CP02 cage plate. Affix a TR2 optical post to the CP02 cage plate (holding the lens). Slide in the lens assembly along the optical rail.
		Mount the CCD camera: Affix a TR2 optical post directly to the CCD camera plate using the 1/4-20 set screw. Slide in the camera assembly along the optical rail. Connect the CCD to the computer using a red ethernet cable. Power up the CCD using the Calrad 45-601 power adapter.
Vertically align the LED, object, lens, and camera assemblies. Make sure the heights of the components are adjusted so your light is going through the object and the lens. Also check that the camera height and angle are appropriately positioned to receive the image of the object.

Visualize, capture, and save images in Matlab

Now that you've learned the basics of mounting, aligning and adjusting optical components, you will through this lab exercise

• verify the lens maker and the magnification formulae:

$ {1 \over S_o} + {1 \over S_i} = {1 \over f} $

$ M = {h_i \over h_o} = {S_i \over S_o} $

• become familiar with image acquisition and distance measurement using the Matlab software.

Log on to the computer, launch Matlab, and run imaqtool. Select the Manta_G-032B(gentl-1) Mono 12" hardware in the left bar. The Start Preview button will bring up a window of the live image from the CCD camera. Move the lens and USAF 1951 target object to produce a focused image. Start with the USAF 1951 target at the 2$ f $ position, i.e., 70 mm from the lens. Divide additional images into an equal number with the target, the object, placed at less than and greater than 2$ f $ from the lens Under the Device Properties tab, optimize the Exposure Time Abs field for good contrast without pixel saturation. Measure the distance $ S_o $ from the target object to the lens and the distance $ S_i $ from the lens to the CCD active imaging plane. Does the lens maker formula $ {1 \over S_o} + {1 \over S_i} = {1 \over f} $ apply as it should when the image focus is optimized?

Save images in Matlab: Make sure you limit to 1 the number of Frames Per Trigger in the General tab of the Acquisition Parameters; Use the Start Acquisition and Export Data buttons; Navigate to the CourseMaterials\StudentData\Fall 2015\ directory accessible from the computer desktop to save your data files remotely on a server you'll be able to browse from your home computer. Recall from one of the initial Stellar announcements that you must use your kerberos ID, preceded by win\, as your username. For example, Professor Nagle would enter "win\sfnagle". Use your kerberos password as well. Remember to disconnect the mapped drive when you are done at your lab station, or log out of the Windows session entirely. The file extension will be .MAT (e.g. 1951target_01.mat), although this extension will not be visible in the Windows Explorer. The variable within this file (e.g. im01) will represent the image as a 492x656 matrix of 16-bit integers.

Examine images in Matlab

	To display the image in Matlab, use the imshow command: In Matlab, open your saved image file ('1951target_01.mat') from the Student Data\ Fall 2015\ directory. Its contents 'im01' now appear in your workspace. When the 12-bit numbers from the camera get transferred to the computer, they are converted to 16-bit numbers. 16-bit numbers can represent a range of values from 0-65535. This leaves a considerable portion of the number range unoccupied. Because of this, if you type imshow( im01 ), you will see an image that looks almost completely black. Adjust the image to fill the full range by typing imshow( 16.0037 * im01 ). Note: 16.0037 equals 65535 / 4095. This factor maps values in the range 0-4095 to 0-65535.
	Determine the distance (in pixels) between two specific points in the image: Either use the Data Cursor Tool and some trigonometry to display the X and Y coordinate of your mouse pointer; or type imdistline on the console to make a very useful measuring tool appear on the image (recommended); or use the interactive improfile function from the Matlab command window, which lets you trace a segment across the active figure (visualized as a dotted line) and generates a plot of pixel intensity vs. pixel position along the segment in a new figure. This manipulation allows you to calculate the image size $ h_i $, taking into account the CCD pixel size: 7.4 μm x 7.4 μm. Confirm the corresponding object size $ h_o $: Refer to the specification sheet of the USAF 1951 test target, pages 5 and 8 in particular. The 1" R1DS1N 1951 USAF test target includes elements of groups 2 and 3. Example: Element 2 in Group 2 has 4.49 cycles (= line pairs) per millimeter. So 2 line pairs from Element 2 in Group 2 span 2 ÷ 4.49 = 0.4454 mm = 445.4 μm. Do both magnification relationships $ M = {h_i \over h_o} = {S_i \over S_o} $ match ?

Plot and discuss your results

• Repeat these measurements of $ S_o $, $ S_i $, $ h_o $, and $ h_i $ for several values of $ S_o $.
• Plot $ {1 \over S_i} $ as a function of $ {1 \over f} - {1 \over S_o} $.
• Plot $ {h_i \over h_o} $ as a function of $ {S_i \over S_o} $.
• What sources of error affect your measurements?
• Given the sources of error, how far off could your measurements of magnification be?

Once you are done with your measurements, please clean up and put back all the parts.

Optical microscopy lab

Code examples and simulations

• Converting Gaussian fit to Rayleigh resolution
• MATLAB: Estimating resolution from a PSF slide image
• Matlab: Scalebars
• Calculating MSD and Diffusion Coefficients

Background reading

• Geometrical optics and ray tracing
• Physical optics and resolution
• Optical aberrations
• Aperture and field stops
• Optical detectors, noise, and the limit of detection
• Manta G032 camera measurements
• Understanding log plots