Optics Assembly Design Document

7/24/2019 Optics Assembly Design Document

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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

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