N A S A G O D D A R D S P A C E F L I G H T C E N T E R I n s t r u m e n t S y n t h e s i s a n d A n a l y s i s L a b o r a t o r y APS Formation Sensor Optics Dennis Charles Evans 15 March 2002

Optics I n s t r u m e n t S y n t h e s i s a n d A n a l y s i s L a b o r a t o r y Dennis Charles Evansp215 March 2002APS Formation Sensor Optical Studies Optical Design Centroid Error Modeling Summary Back-up Information

Optics I n s t r u m e n t S y n t h e s i s a n d A n a l y s i s L a b o r a t o r y Dennis Charles Evansp315 March 2002APS Formation Sensor Optical Characteristics Telecentric Design (Modified Aerial Mapping Camera) – Changes in length do not change plate scale Aperture = 100 mm (selected) Optical Speed = f/5 (selected for ease of fabrication) – Focal Length = 500 mm (result) Optical Design Half Angle FOV = 5.0 degrees (larger angles possible) Plate Scale Needed for Point Design – Based on deployed element distribution – 5 km at 50 km (source) = 50 mm at 500 mm (focal plane) – 4096×0.013 = mm typical detector – Half angle = 2.9 degrees – The tracker could handle a wider distributed source by using a larger detector or series of detectors. Glasses: Schott SK4, F 5, LF 5 – May have to replace with radiation hard glasses Design is internally baffled only – An external sunshade may be needed for a particular instrument

Optics I n s t r u m e n t S y n t h e s i s a n d A n a l y s i s L a b o r a t o r y Dennis Charles Evansp415 March 2002APS Formation Sensor Tolerance Analysis (not done, not expected to be a problem) – Design was selected to be insensitive to changes in focus. Thermal characteristics similar to CHyMERA. – Thermal changes in index of refraction change focus more than mechanical expansion of lens holder. – A matched lens holder coefficient of expansion will not make an thermally insensitive design. – CHyMERA required near zero CTE (GFRP) because of thermal gradients perpendicular to optical axis (banana effect) – Commercial Tilts & Decenters acceptable Implications – Proportional Thermal Controller (±3 degree C range) – Would like Lenses near ambient and Detector near 0  C for simplicity detector housing should be above freezing Optical Characteristics

Optics I n s t r u m e n t S y n t h e s i s a n d A n a l y s i s L a b o r a t o r y Dennis Charles Evansp515 March 2002APS Formation Sensor Ghost images will result from reflections at lens and filter surfaces – Filter ghosts will be centroid aligned with beacon image Filter ghost will be of image or lower – Lens ghosts will be generally diffuse Reference to other designs implies lens ghosts will be to of image or lower. Flat Field Monitoring is provided by illuminating a diffuser plate on the back of the closed aperture door Wavelength filters are needed for resolving multiple beacons on same daughter or daughters very close together. – depending on stability, beacons could be turned off and on for identification and angular separation Optical Characteristics

Optics I n s t r u m e n t S y n t h e s i s a n d A n a l y s i s L a b o r a t o r y Dennis Charles Evansp615 March 2002APS Formation Sensor Telecentric Aerial Photo Lens SK4 F5 LF5 SK4 = 3.57 g/cc F5 = 3.47 g/cc LF5 = 3.22 g/cc 100 mm diameter Telecentric Stop

Optics I n s t r u m e n t S y n t h e s i s a n d A n a l y s i s L a b o r a t o r y Dennis Charles Evansp715 March 2002APS Formation Sensor Defocused Spots for Centroiding

Optics I n s t r u m e n t S y n t h e s i s a n d A n a l y s i s L a b o r a t o r y Dennis Charles Evansp815 March 2002APS Formation Sensor AutoCAD 3D Model

Optics I n s t r u m e n t S y n t h e s i s a n d A n a l y s i s L a b o r a t o r y Dennis Charles Evansp915 March 2002APS Formation Sensor Basic Mounting & Internal Baffle Layout Defining 100 mm diameter Telecentric Stop Detector Pseudo Stop Aperture

Optics I n s t r u m e n t S y n t h e s i s a n d A n a l y s i s L a b o r a t o r y Dennis Charles Evansp1015 March 2002APS Formation Sensor Centroid Error Modeling Uniform Defocused Image Model Photoelectron Random Normal Statistics

Optics I n s t r u m e n t S y n t h e s i s a n d A n a l y s i s L a b o r a t o r y Dennis Charles Evansp1115 March 2002APS Formation Sensor Centroiding Model Results Electro-Optical system throughput was calculated for sec cycle. 3 x 3 and 9 x 9 pixel centroiding with PE/px, integrated for 10 cycles (0.01 sec), results in noise statistics about 5 x better than the arc-sec error needed. For 1000 cycle averaging, the centroid error is arcsecond; equivalent to mm at 50 km, much better than the basic requirement. A significant noise margin exists for the point design! The margin on noise can be greatly improved if needed. Noise is reduced most effectively by increasing the number of PE/px. Well depth is being improved for APS arrays. CCD arrays have an order-of-magnitude deeper wells at present.

Optics I n s t r u m e n t S y n t h e s i s a n d A n a l y s i s L a b o r a t o r y Dennis Charles Evansp1215 March 2002APS Formation Sensor Centroiding Noise Model

Optics I n s t r u m e n t S y n t h e s i s a n d A n a l y s i s L a b o r a t o r y Dennis Charles Evansp1315 March 2002APS Formation Sensor Centroiding Error Sensitivity Pixel Size (mm) Pixel Size (arc-sec) Centroid ErrorArc-Sec Error pixel pixel pixel pixel pixel

Optics I n s t r u m e n t S y n t h e s i s a n d A n a l y s i s L a b o r a t o r y Dennis Charles Evansp1415 March 2002APS Formation Sensor J[40 000PE/px, 9x9, 1 Cycle Average]

Optics I n s t r u m e n t S y n t h e s i s a n d A n a l y s i s L a b o r a t o r y Dennis Charles Evansp1515 March 2002APS Formation Sensor J[40 000PE/px, 9x9, 3 Cycle Average]

Optics I n s t r u m e n t S y n t h e s i s a n d A n a l y s i s L a b o r a t o r y Dennis Charles Evansp1615 March 2002APS Formation Sensor J[40 000PE/px, 9x9, 10 Cycle Average]

Optics I n s t r u m e n t S y n t h e s i s a n d A n a l y s i s L a b o r a t o r y Dennis Charles Evansp1715 March 2002APS Formation Sensor J[40 000PE/px, 9x9, 1000 Cycle Average]

Optics I n s t r u m e n t S y n t h e s i s a n d A n a l y s i s L a b o r a t o r y Dennis Charles Evansp1815 March 2002APS Formation Sensor Wide Flux Design Range Electro-Optical system throughput was evaluated at second cycle rate, not 1 second. System time constant is likely to be in the seconds to minutes range. Position requirement of 3 mm at 50 km was arcsecond Integration of Centroid for 1000 cycles gives a position error of pixel width (1/22 of design goal) Centroid error is arcsecond; equivalent to mm at 50 km. Implication: – System has more capability than required – Could be reduced in size by an order-of-magnitude in volume

Optics I n s t r u m e n t S y n t h e s i s a n d A n a l y s i s L a b o r a t o r y Dennis Charles Evansp1915 March 2002APS Formation Sensor Optical Performance Summary Thermally stable Telecentric Optical Design – analytically attractive – flight proven design concept Position error due to photoelectron statistical noise is well below the arcseconds needed for this design If 3mm error at 50km is all that is needed, the size of the sensor system might be reduced significantly, possibly by a factor of 10 in mass.

Optics I n s t r u m e n t S y n t h e s i s a n d A n a l y s i s L a b o r a t o r y Dennis Charles Evansp2015 March 2002APS Formation Sensor Back-up Information

Optics I n s t r u m e n t S y n t h e s i s a n d A n a l y s i s L a b o r a t o r y Dennis Charles Evansp2115 March 2002APS Formation Sensor Aerial-02.ZMX Prescription #TypeComment Curvature (1/mm) Radius (mm) Thickness (mm)Glass Semi- DiameterConic 0STANDARD 0.00E+00 10^ STANDARDTELECENTER0.00E STANDARDL1F3.31E SK STANDARDL1B9.18E STANDARDL2F6.02E SK STANDARDL2B-8.31E STANDARDL3F-7.37E F STANDARDL3B9.36E COORDBRK 0.00E STANDARDINTERNAL STOP0.00E COORDBRK 0.00E STANDARDL4F-8.21E LF STANDARDL4B1.09E STANDARDL5F1.12E SK STANDARDL5B-5.90E STANDARDL6F1.08E SK STANDARDL6B-2.13E COORDBRK 0.00E STANDARDBEST FOCUS0.00E COORDBRKDEFOCUS 10.00E STANDARDIMAGE0.00E

Optics I n s t r u m e n t S y n t h e s i s a n d A n a l y s i s L a b o r a t o r y Dennis Charles Evansp2215 March 2002APS Formation Sensor Lens Element Mass ELEMENT VOLUME DATA: Values are only accurate for plane and spherical surfaces. Element volumes are computed by assuming edges are squared up to the larger of the front and back radial aperture. Volume cc Density g/cc Mass g Element surf 2 to Element surf 4 to Element surf 6 to Element surf 11 to Element surf 13 to Element surf 15 to Total Mass:

Optics I n s t r u m e n t S y n t h e s i s a n d A n a l y s i s L a b o r a t o r y Dennis Charles Evansp2315 March 2002APS Formation Sensor Photo Electron Noise Modeling Photo Electron Noise is related to the square root of the signal. The square root of the signal is approximately 1 sigma deviation. The noise is modeled as a Normal (Gaussian) distribution with a one sigma standard deviation equal to the square root of the signal. Procedure for generating normal distribution noise – Computer language generates pseudo random number from 1 to 1000 and scales to to – Function converts number to random normal distribution.

Optics I n s t r u m e n t S y n t h e s i s a n d A n a l y s i s L a b o r a t o r y Dennis Charles Evansp2415 March 2002APS Formation Sensor Normal Distribution -5  00 +5  68.3 % 95.5 % 99.7 %

Optics I n s t r u m e n t S y n t h e s i s a n d A n a l y s i s L a b o r a t o r y Dennis Charles Evansp2515 March 2002APS Formation Sensor Random Normal Signal Distribution -5  00 +5  0 1 Selection of random value on vertical axis produces random normal distribution on horizontal axis

Optics I n s t r u m e n t S y n t h e s i s a n d A n a l y s i s L a b o r a t o r y Dennis Charles Evansp2615 March 2002APS Formation Sensor 9 TrackerFocalPlane Centroid is at 12,8 = Array[J;I] A[;1] A[;2] …… Centroiding Model A[1;] A[2;] etc.

Optics I n s t r u m e n t S y n t h e s i s a n d A n a l y s i s L a b o r a t o r y Dennis Charles Evansp2715 March 2002APS Formation Sensor Centroiding Model Numerical Sample Image Size (pixels) PE/Pixel Centroid (pixels) 10 Sample Analysis 3 x sample low 10 sample mean 1 sample high sample low 10 sample mean 1 sample high sample low 10 sample mean 1 sample high

Optics I n s t r u m e n t S y n t h e s i s a n d A n a l y s i s L a b o r a t o r y Dennis Charles Evansp2815 March 2002APS Formation Sensor Image Size (pixels) PE/Pixel Centroid (pixels) 10 Sample Analysis 9 x /9 = sample low 10 sample mean 1 sample high sample low 10 sample mean 1 sample high sample low 10 sample mean 1 sample high Centroiding Model Numerical Sample

Optics I n s t r u m e n t S y n t h e s i s a n d A n a l y s i s L a b o r a t o r y Dennis Charles Evansp2915 March 2002APS Formation Sensor A Design with Filter & Lens Ghosts

Optics I n s t r u m e n t S y n t h e s i s a n d A n a l y s i s L a b o r a t o r y Dennis Charles Evansp3015 March 2002APS Formation Sensor Typical Reflection Ghosts Floor at 1E-6 Near ghost between 1/1000 and 1/10,000. “Diffuse” lens ghosts.

Optics I n s t r u m e n t S y n t h e s i s a n d A n a l y s i s L a b o r a t o r y Dennis Charles Evansp3115 March 2002APS Formation Sensor Floor at 1E-4 Near ghost is about 1/600. General ghosts between 1/600 to 1/1000. All look like surface ghosts. Typical Lens & Filter Reflection Ghosts