optics assembly design document
TRANSCRIPT
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Star sensor design report
Design Goals:
A star sensor to calculate attitude of a satellite with an accuracy of
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Surf Radius Thickness GlassSemi
diameter
OBJ Infinity Infinity
1 61.625060 8 H-K9L 15
2 323.713828 10 15
3 -43.812408 8 H-F13 15
4 -58.496670 5 15
STO Infinity 5 14.089662
6 90.950408 4 H-F13 15
7 26.827345 0 15
8 26.827345 8 H-K9L 15
9 -70.946491 65.343035 15
IMA Infinity 7.5
Table 1. Lens data
Optical properties of the lens
Minimum number of stars in the field 5 stars
Limiting magnitude 6.5 m at 2 detection level
Field of view 10 degrees
Focal length 80 mm
Entrance aperture 30 mm
We have chosen a lens system for compactness and ease of acquisition.
The entrance aperture is defined to be 30 mm by the sensitivity limit of 6m.5. (Appendix
A)
The optics design is shown in Fig. 1 and the lens data is listed in Table 1. We have baselined a tessar lens which is a 4 element design with a stop after the
second element. This arrangement provides 8 independent variables (6 radii of
curvatures and 2 inter-element distances) which are enough to control 7 primary
aberrations (5 third order seidel aberrations and 2 first order chromatic
aberrations).
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The glasses are selected from the CDGM catalog (one of the catalog from a glass
manufacturing company named CDGM) and were chosen in consultation with
manufacturers to ensure their availability. A suitable combination of crown and
flint glasses reduces chromatic aberrations.
Fig. 2. Spot diagram Fig. 3. Encircled energy
The spot diagram is shown in Fig. 2 and the encircled energy in Fig. 3.
We have chosen a detector (see below) with a pixel size of 15 m. We desire the
PSF to spread over a 3x3 pixel box for accurate centroiding implying a spot size ~22 m. At least 50% of the encircled energy should be within the central pixel.
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Fig. 4. Line and edge graph (0 degrees field) Fig. 5. Line and edge graph (5 degrees field)
The line graph shows the profile of the spot integrated over the wavelength range
(400-700nm) in both tangential and sagittal directions (x-y directions) on the image
plane. The edge graph shows the integrated profile of the line graph. The sudden jump inthe edge graph at the centre point shows that most of the incident energy is concentrated
in the centre of the spot.
Fig. 6. Field curvature and distortion graphs
Distortion plays an important role in the star sensor working. It causes the centroids of
the stars in the image to shift from their ideal locations on the image plane. This reflects
in error in attitude estimation by the algorithm. The distortion graph shows that the
maximum distortion of the image due to the optics is only 0.1% which is very small.
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Detector
We have chosen the Star 1000 CMOS sensor. This is a radiation hardened sensor that has
been used in many space missions. The datasheet of the detector can be found here.
With the advent of fast electronic technology it is possible to achieve the fast update rate
of 10Hz for the star sensor. The frames need to be taken at speeds faster than 10Hz to
keep enough time for the image processing. Hence the maximum integration time for the
detector is limited by this update rate criterion and is assumed to be 50ms considering
remaining time of 50ms for calculating the attitude.
This detector was selected because of the following characteristics:
Rolling shutter and region of interest readout possibility: Useful for fast data
acquisition in the tracking mode of the star sensor.
Radiation hardening: Gives long life time for the detector.
http://www.onsemi.com/pub_link/Collateral/NOIS1SM1000A-D.PDF -
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Assembly:
In the design procedure we need to consider the optics which includes the lenses and the
detector system as well as the mechanical assembly for holding the optics and keeping it
intact in the adverse conditions of space and during the launch. The optics involves 4 lenses with one cemented doublet in line followed by a distance to
the detector as shown in Fig.1. To implement such a design the mechanical assembly may
be built in a way as shown in Fig. 2.
Fig. 1. Optical design of the lens
Fig. 2. General layout of lens assembly
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Here we talk about the lens tube as shown in the stick diagram above. This part of the
assembly is to be manufactured along with the lenses. The lenses are assembled together
in a lens tube.. The cross section of the lens tube is as shown in Fig. 3. The Y axis points
to the longitudinal direction and the X and Z axes point in the transverse direction of the
lens.
Fig. 3. Cross section of Lens tube
This lens tube fits on a lens table which connects the star sensor to the satellite body.
The detector goes under the lens table at an adjustable distance and the electronics
including the detector data acquisition fpga and the star sensor controller goes on a pcb
behind the detector. A baffle prevents the stray light reaching the sensor.
The mechanical data for the glasses are as shown in the table:
Lens Glass Glass
density
Radius Thickness Volume Mass
Lens 1 H-K9L 2.52gm/cm3 15mm 8mm 5654 mm3 14.2481gm
Lens 2 H-F13 2.63gm/cm3 15mm 8mm 5654mm3 14.8722gm
Lens 3 H-F13 2.52gm/cm3 15mm 4mm 2827mm3 7.1251gm
Lens 4 H-K9L 2.69gm/cm3 15mm 8mm 5654mm3 15.2115gm
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The parameters of the tube are :
Material Aluminium
Density 2.7gm/cm3
Length 57mm
Thickness 5mm
Radius 34mm
Volume 11800mm3
Mass 32gm
To hold the lenses and stop at their desired positions and for load bearing there are
spacers and washers respectively. The schematic diagrams of each of them are as shownin the figures followed.
Fig. 4. Spacer
Fig. 5. Washer
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The washer acts as cushions between any two surfaces. The interface between any
surface and the washer is through the 3 protrusions as shown in the figure 5. The ring
between the protrusions flexes when there is a force applied by any surface on the other
and hence attenuates the effect of the applied force. This kind of construction also
compensates for temperature based stresses generated due to the expansion or contraction
of each surfaces.
Given the mass of the glass and the lens tube from the tables above, the value of
maximum force that can act on any glass surface is around 10N considering 20g of
acceleration.
Two parameters related to the washer are to be calculated:
Minimum contact area of the protrusions
Minimum thickness of the washer to facilitate proper flexure
Minimum contact area is found by considering 10N force applied on the glass, given the
knoop hardness of the glass (essentially the measure of the limiting stress at which the
glass shatters). We know the width of the washer which is supposed to be 2mm to hold
the glasses and spacers properly. Hence the arc length of the protrusion can be calculated.
Minimum thickness of the washer is estimated by modelling it as a simply supported
beam supported at two ends and force acting between the supports. The maximum flexure
calculated for given force values defines the minimum clearance the washer should give
for the flexure.
Fig. 6. Simply supported beam model
Minimum contact area 2 x 10-8 mm2
Length of the protrusion 10-2mm
Minimum thickness of washer 2um
These values are so small that they are unrealisable which means the forces dealt with are
pretty small. Hence the design is made using reasonable values larger than calculated
values.
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The washer is to be made with teflon to give soft contacts with the glass. Teflon has very
low outgassing properties (TML - 0.05% and CVCM - 0.00%). To select a sample with
low outgassing TML
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Appendix A
Requirement for Limiting magnitude of 6
m
.5
Aperture size
Lmag = 2 + 5log(D0)
Lmag is the limiting magnitude required and D0is the minimum entrance aperture of the
optics.This gives D 0
~ 10mm for 6 m stars but considering the sensitivity of the detector we
keep a margin and define the required entrance aperture as 25mm.
Detector sensitivity verification
To verify that the limiting magnitude of optics is 6m.5 we find the number of
electrons generated in the detector by a
6m.5star and compare it with the noise
electrons. This ratio should be atleast 5 times (which is set as threshold) for a
successful detection of a star.
To calculate the number of electrons from a 6m.5star we find the flux of the star
in photons/cm2/sec. This is obtained from the definition of magnitude of star
compared to Vega which is a 0 mag star.
m1- m2= -2.5 log (F1/F2)
where F 1 and F2
are the fluxes from the stars with magnitudes m1 and m2
respectively.
Flux from 6.5 mag star 33480 photons/cm2/sec
Geometrical collecting area 7.0685 cm2
Maximum integration time 100ms
Transmission efficiency of each lens 90%
Number of lenses 4
Total transmission efficiency 65%
Quantum efficiency x Fill factor 30%
Pixel efficiency 50%
Number of signal electrons generated ~3500 e-
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Detector noise characteristics as obtained from the datasheet are as shown in the
table:
Temporal 62.6087 e-
Global 668.5217 e-
Dark Signal (for 50ms) 122.6087 e-
Dark Signal Non Uniformity 1423.304 e-
Photo Response Non Uniformity 540.6331 e-
Total Noise 1668.518 e-
Signal corresponding to 6.5 mag (for
50ms)
3500 e-
SNR 2.1
Hence the signal to noise ratio obtained is 2.1 which is as required and thus the
limiting magnitude of the instrument can be safely assumed to be 6.5 mag
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Appendix B
Field of view calculations and sky maps
The field of view of the optics required to satisfy this criterion of 5 stars for 6.5m limiting
sky is 10 degrees. A simulation of different field of views and the percentage of sky notsatisfying the condition is as shown below.
FOV in degrees %
6 14
7 2.8
8 0.5345
9 0.0636
10 0.0030