The Compton Spectrometer and Imager (COSI) is a soft γ-ray (0.2 ~ 10
MeV) telescope with twelve germanium detectors (GeDs), which are designed to
detect the cosmic γ-ray photons by using the Compton scattering technique to
locate the incident photons. A coded mask technique is planned to be applied on
this instrument, so that the incoming non-scattered photons below 200 keV can
be imaged instead of being excluded in the existing Compton imaging approach.
The imaging capability of COSI is then expected to extend to the hard X-ray
band (40-100 keV) to enable more possibilities on scientific purposes.
With a basic mask pattern designed for COSI, which is a 33×31 pixels array
with a pixel size of 2× 2 mm2 (the spatial resolution of the GeDs is 2 mm), we set up a data reduction pipeline for the coded mask pattern and tested the an-
alytic method by performing Monte-Carlo simulations to get the instrumental
parameters and found the best-performed mask geometry and material. The
effects from the Caroli-factor and pixel shuffling were considered in the simula-
tions. From the simulation results, we decided to use Tin (Sn) which absorbs
effectively below 100 keV but is well transmitted at high energy range, as the
mask material.

Table of Contents i
List of Figures iii
List of Tables v
1 The Compton Spectrometer and Imager (COSI) 1
1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Germanium Detectors of COSI . . . . . . . . . . . . . . . . . . 2
1.3 Compton Scattering Image . . . . . . . . . . . . . . . . . . . . . 3
1.4 Balloon Flights and Current Status . . . . . . . . . . . . . . . . 3
2 Coded Mask Technique 7
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.2 Coded Mask . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.2.1 Recovering the sky image - Deconvolution . . . . . . . . 9
2.2.2 Recovering the sky image - Correlation . . . . . . . . . . 10
2.3 Coded Mask Design for COSI . . . . . . . . . . . . . . . . . . . 11
2.3.1 Uniformly Redundant Array (URA) . . . . . . . . . . . . 11
2.3.2 The URA Pattern for COSI . . . . . . . . . . . . . . . . 13
2.3.3 Field of View . . . . . . . . . . . . . . . . . . . . . . . . 16
2.3.4 Pixel Shuffling . . . . . . . . . . . . . . . . . . . . . . . . 18
3 Simulations and Results of COSI Coded Mask 22
3.1 Simulation Process . . . . . . . . . . . . . . . . . . . . . . . . . 23
3.2 Simulation Results . . . . . . . . . . . . . . . . . . . . . . . . . 25
3.2.1 Mask Absorption effect . . . . . . . . . . . . . . . . . . . 25
3.2.2 Collecting Ratio . . . . . . . . . . . . . . . . . . . . . . . 27
3.2.3 Angular Resolution . . . . . . . . . . . . . . . . . . . . . 28
3.2.4 Sensitivity . . . . . . . . . . . . . . . . . . . . . . . . . . 32
3.3 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
3.3.1 Position Accuracy . . . . . . . . . . . . . . . . . . . . . . 37
3.3.2 Caroli Factor . . . . . . . . . . . . . . . . . . . . . . . . 38
3.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

Ables, J. G. 1968, Proceedings of the Astronomical Society of Australia, 1, 172
Bandstra, M., Bowen, J., Zoglauer, A., et al. 2006, in Nuclear Science Sympo-
sium Conference Record, 2006. IEEE, Vol. 2, 770–777
Bandstra, M. S., Bellm, E. C., Boggs, S. E., et al. 2011, ApJ, 738, 8
Bowen, J. D. 2009, PhD thesis, University of California, Berkeley
Cannon, T. M., & Fenimore, E. E. 1979, Appl. Opt., 18, 1052
Caroli, E., Stephen, J. B., Di Cocco, G., Natalucci, L., & Spizzichino, A. 1987,
Space Sci. Rev., 45, 349
Chan, Y., Siu, M., & Tong, P. 1979, Information and Control, 42, 125
Chou, Y. 2008, Instruments Today, 30, 36
Churazov, E., Sunyaev, R., Revnivtsev, M., et al. 2007, A&A, 467, 529
Dicke, R. H. 1968, ApJ, 153, L101
Fenimore, E. E., & Cannon, T. M. 1978, Appl. Opt., 17, 337
MacWilliams, F., & Sloane, N. J. A. 1976, Proceedings of the IEEE, 64, 1715