Content
- Welcome
- Abstract
- Introduction
- Methods and Materials
- Finding the Theoretical Limit
- The Two Lenses: Collimator and Diffraction
- Testing the Theoretical Limit
- Final Projector Parts
- Protector
- Main Body
- End Piece
- Improvements
- Final Projector Tests
- Results
- Discussion
- Acknowledgements
- References
Welcome
This page presents my research paper submission to the Intel STS International Competition in 2008. The Department of Energy needed to develop a laser to test camera hardware (CCDs) for the worlds largest digital camera (LSS Telescope).
Note 1: A CCD essentially determines a digital cameras resolution and sensitivity. In order to study the stars we need the highest quality CCDs.
Note 2: The laser needed to have a focus point under 1 micron (millionth of a meter). Average hair thinkness is 800 microns.
Abstract
This paper presents the mathematical model and design of the Point-Spread Function (PSF) Projector needed to check the Charge-Coupled Devices (CCDs) of the Large Synoptic Survey Telescope (LSST). The comparison of the produced device vs the math model properties is present as well. The LSST, and its 3.2 Giga pixel CCD array will undertake a wide angle, deep survey of the entire southern sky starting in 2014 (Postponed to 2023). The survey database will support a wide variety of astrophysical investigations, with particular emphasis on elucidating the nature of dark energy [1]. Composed of 189 CCD sensors [estimated at $100k each] to be selected from one of three manufacturers, the array will be massive, efficient, and accurate. Today, the building of the CCD test and Focal Plane assembly facility is underway at Brookhaven National Laboratory (BNL), one of the nations’ best research facilities. For CCD testing a spot projector is needed to focus a laser beam into the smallest possible diameter, on the CCD surface. Such a set up allows studying the CCD point-spread function: the broadening of the spot caused by diffusion of charge carriers on their way from the CCD window to the collecting electrodes. The expected broadening is on the order of 3-4 microns. To see this effect, the spot size should be under one micron. The paper presents the design of the projector to achieve the smallest possible spot and test results that show the desirable spot size was achieved.
Introduction
The LSST has been identified as a national scientific priority in reports by several National Academy of Sciences and federal agency advisory committees. This judgment is based upon the LSSTs ability to address some of the most urgent open questions in astronomy and fundamental physics, while driving advances in data-intensive science and computing. The National Academy of Sciences “Quarks-to-Cosmos” report recommended the LSST as an incisive probe of the nature of dark energy. The LSST will open a new frontier in addressing time variable phenomena in astronomy. The focal plane array composed of 189 CCDs will provide the cameras massive resolution. Each CCD has to pass rigorous requirements, and the Point-Spread Function (PSF) [2] is one of them. For the PSF studies to be accurate a precise laser spot has to be projected onto the CCD about the size of one micron. An optical projector had to be built for this. This projector will help Instrumentation with accuracy of data, save time and allow the CCD array of LSST project to be completed in time.
The BNL Instrumentation Division is responsible for designing the framework to test the CCD sensors needed to build LSST 3.2 billion pixel digital camera, the largest ever created. This is a unique system for surveying the heavens that is made possible by advances in several technologies.
My assignment was to produce a mathematical model to calculate the projector property, test a prototype projector to see if the real projector properties and the theoretical properties match, then depending on the results redesign a final version with minimal flaws.
Methods & Materials
Finding the Theoretical Limit
This formula [3] is the mathematical model of the phenomena inside of the projector
This first formula gives the intensity of the Fraunhofer diffraction pattern. Where Io is the maximum intensity of the pattern at the airy disc center, k=2(pi) / lambda is the wavelength, d is the diameter of the diffraction lens and Theta is the angle of observation, i.e. the angle between the axis of the circular aperture and the line between aperture center and observation point.
Next the formulas below give the angle at which the first minimum occurs, measured from the direction of incoming light [3].
I synthesized these formulas together to get the theoretical limit formula
The result from our prototype projector was 0.48um. Suitable for PSD studies. (Image 1.0)
Due to this conclusion, if a device with the provided lenses was built to ideal specifications, it would have a minimal focused spot size of 0.48um in diameter.
The Two Lenses: Collimator and Diffraction
The Instrumentation Division was supplied with a collimator lens Mitutoyo M – L/1x. This lens was placed 200mm in front of the fiber optic for optimal efficiency. After the light passed through the lens all the rays became parallel. That is why the distance between the two lenses is not significant, and wouldn’t affect anything. The only requirement was to keep the two lenses parallel to each other.
The second lens was the Diffraction Limited Focusing Lens Mitutoyo 10x. It took the parallel rays and diffracted them back with a focus point at 3cm. The diffraction lens also needed to be protected since it was an expensive piece and any slight scratch or even finger prints could skew the data.
The lab setup was within a “clean room”, where shoe covers had to go over your shoes. The CCD was placed into a vacuum cylinder and cooled with liquid nitrogen to mimic the future environment of the telescope. One of the walls in the vacuum cylinder was replaced with a half inch thick fused silica window to let the laser from the projector shine onto the CCD. On the other side of the chamber, the projector was within a black box to minimize stray light from interfering with the laser light. Then the projector was mounted onto a mechanical arm that could move in increments of one micron for precision on a x-y-z plane.
Testing the Theoretical Limit
The theoretical limit still needed to be tested in the real world which would possibly reveal unseen changes. A prototype was constructed out of Microbench parts [4], since Microbench provided many of the essential tools for optical work. (Image 1.1)
The goal of the prototype design was to test the accuracy of the theoretical properties to the real properties. On one end, the diffraction Lens screwed in, in the middle there was a slot of the collimator lens and on the end there was a fixed adapter for the fiber cable, approximately 200mm from the collimator lens.
The prototype was tested in at a different lab set up than the CCDs. The projector was fixed onto a table, and then shined the laser into a 20x scope and into a specialized camera hooked up to a computer. The focus could be adjusted by fine and rough tuners on the 20x scope. The results were recorded as a snapshot (Image 1.2). The resolution can also be seen in this graph (Image 1.3) [11]. According to the picture and the graph the spot size (R.M.S.) was 0.78 microns, suitable for PSF studies.
Due to the reliable test results from the prototype a final version had to be designed and built. Using AutoCAD ’09 I was able to produce sketches quickly and accurately which was essential for the Instrumentation test to meet deadlines for.
Final Projector Parts
Protector
The purpose of the designed protector (Sketch 1.0) is to protect the expensive diffraction lens from any accidental unit movements into adjacent walls or glass protecting the CCD (Image 1.4). It spanned the full length of the lens sticking out from the main body, but only longer by 1.0mm to not sacrifice focus area, yet maximize protection.
Main Body
The main body of the projector held both lenses safely, securely, and accurately (Image 1.5). The lenses had to be parallel to each other (Sketch 1.1). After light passed through the collimator lens the rays become parallel and have to stay that way as they passed into the diffraction lens.
To provide stability and room for flexibility to move the lens accurately if needed, 3 pairs of fine threaded holes were bored for screws around the slot where the collimator lens was to be placed. Each paired hole was 120 degrees apart for optimal coverage of control of flexibility, and the holes were paired for stability versus single holes. Also, two standard quarter inch holes were threaded on one side for the mounting plate to screw unto the mechanical arm
End Piece
The final end piece (Image 1.6) is just as important as the rest, and held the critical distance derived from the mathematical formula. One side of the end piece screwed into the main body while the other held the fiber optic providing the light. The critical distance between the fiber tip to the collimator lens was calculated to be 200cm (Sketch 1.2). This distance will result in the optimal coverage of the circumference of the collimator lens by the fiber. Room for flexibility was provided at the fiber side. There was an adapter that connected the fiber and the end piece together. It could also be screwed in or out by 20mm adjustments to the critical distance, and then secured with an end cap by either screwing in before or after the adapter to eliminate the adapter movement after placement.
Improvements
After numerous examinations, two most significant and critical improvement were administered for the accuracy of the projector: black anodizing and placing a baffle in the “end piece”. The projector was “light-tight” and was decided to be built out of solid aluminum for its light weight and quick sculpting characteristics.
However, the aluminum contains reflecting properties, so the light produced within the projector, if not constrained properly may affect the accuracy. By black anodizing the entire projector most of the light that hits the walls will be absorbed [1].
Next, the baffle (Image 1.7) was designed. The purpose of the baffle was to limit light that may potentially bounce off walls and only allow direct light from the fiber to the collimator lens (Image 1.8). That is made possible by making the baffle half the size of the circumference and placing it in the middle of the “end piece” . It effectively and accurately blocks out possible light that will interfere by bouncing off the walls. Also, be designing the side of the baffle facing the fiber with a knife edge, it effectively blocked potentially harmful light back into the chamber towards the fiber.
The device was manufactured and black anodized by BNL shop according to the sketches prepared with AutoCAD.
[1]1 For the purposes of presentation, all projector pictures were taken before black anodizing
Final Projector Tests
The final projector was tested the same way as the prototype. The size of the spot was 0.53 micron (R.M.S.) and suitable for PSF studies. As seen in Image 1.9[11] and Image 2.0 [11] the spot size is better than the prototype and closer to the theoretical limit.
Next the projector had to go through an additional test. In the lab setup for CCD testing, the CCD will be placed into a vacuum, and cooled with liquid nitrogen, while the laser shines from outside the vacuum. That is made possible by placing a half inch fused silica window on one side of the vacuum to let the laser shine in. To test if the window would have any effect on the spot size, it was placed perpendicular between the specialized camera and the 20x scope. A snap shot was taken again, and the resolution graphed. (Image 2.1 and Image 2.2 respectively) [11]
According to the test results the spot size had increased from 0.53 microns to 0.88 microns after passing through the window.
Results
Using the Airy Disk formula, the theoretical limit with the diffraction lens was calculated to be 0.48um. This is substantially small enough for PSF testing, which requires the spot to be no larger than 1.0um. Using the mathematical formula calculations, a prototype projector was built to test the theoretical limit. From Image 1.7 and 1.8 it could be seen that the size of the spot is below the maximum allowable size of the spot. Following the prototype testing, the Instrumentation division provided the AutoCAD program to design and sketch a final version of the projector. The critical measurements were taken from the prototype and applied to the final version. Upon finishing the sketches and design, it underwent examinations by department members and improvements were proposed. After the final projector was built it was tested in the same way as the prototype giving a spot size of 0.88 micron after passing through the silicon window.
Discussion
From the Airy Disk formulas, the Fraunhofer formula, and the two lenses, the theoretical limit and properties could be calculated to be 0.48 um, and the 200mm distance from the fiber to the collimator lens. The prototype projector produced reliable test results on the theoretical limit. Following the prototype, the final version of the projector was sketched and revised multiple times before given to the shop to be manufactured. The projector eliminated some faults of the prototype with less parts, less susceptible to vibrations, and significantly reducing the possibility of stray light affecting the test results. It also, produced a 0.53 micron spot size without the silicon window and 0.88 with the window. Both sizes, as previously mentioned, are suitable for PSF studies, even though there is an increase of the spot diameter after passing through the window. The relevantly close numbers of the theoretical limit of 0.48micron to 0.53micron from the final projector confirm accurate designing and manufacturing of the projector. As of now, the optical projector is being used at BNL by the Instrumentation Division for further CCD testing with the PSF and other studies. Brett Morris, a colleague, will use this projector to do PSF studies and “virtual knife-edge” scans to figure out the properties of CCDs [6]. This instrument is a vital part of the LSST project and keeping the team in check for the deadline.
Acknowledgments
This project was possible thanks to the supervision of Dr. Ivan Kotov as my mentor. Dr. Peter Takacs and the rest of the Instrumentation Division for assisting me. The BNL HS Research Program and Scott Bronson as the program director for inviting me. The BNL shop for manufacturing my design sketches. Dr. George Baldo for assisting my participation in the InSTAR Science Research program.
References
[1] “New windows on the Universe.” Large Synoptic Survey Telescope. 31 October 2008. LSST Corporation,. 11 Nov 2008 <http://www.lsst.org>.
[2] “Point spread function.” Wikipedia, The Free Encyclopedia. 11 Nov 2008, <http://en.wikipedia.org/w/index.php?title=Point_spread_function&oldid=251048532>.
[3] “Airy disk.” Wikipedia, The Free Encyclopedia. 8 Nov 2008, 16:06 UTC. 14 Nov 2008 <http://en.wikipedia.org/w/index.php?title=Airy_disk&oldid=250456332>.
[4]”Microbench.” Microbench Sets. LINOS. 14 Nov 2008 <http://www.linos.com/pages/home/shop-mechanik/banksysteme/mikrobank/starten/mikrobank-saetze/>.
[5] Bronson, Scott. Private Communication. July 2008.
[6] E. Hecht, Optics, Addison Wesley (2001)
[7] Fine, Valeri. Private Communication. July 2008
[8] Kotov, Ivan. Private Communication. 08 July 2008.
[9] Morris, Brett. Private Communication. July 2008
[10] O’Connor, et al ” Technology of the LSST focal plane 1 “Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment. August 2007 1-8. 11 November 2008 .
[11]Takacs, Peter. Private Communication. July 2008.
[12]Takacs, Peter. “PSFM spot size with units #1 & #2.”.PowerPoint. Instrumentation Division Conference.10 October 2008.
[13]Zhang et al., Optics Express, 15, 1543-1552 (2007): http://www.opticsexpress.org/abstract.cfm?uri=oe-15-4-1543