Fixed-point vs. floating-point arithmetic comparison for adaptive optics real-time control computation

Yolanda Martín-Hernando; Luis Fernando Rodríguez-Ramos; Marcos Reyes Garcia-Talavera

doi:10.1117/12.787408

10 July 2008 Fixed-point vs. floating-point arithmetic comparison for adaptive optics real-time control computation

Yolanda Martín-Hernando, Luis Fernando Rodríguez-Ramos, Marcos Reyes Garcia-Talavera

Proceedings Volume 7015, Adaptive Optics Systems; 70152Z (2008) https://doi.org/10.1117/12.787408
Event: SPIE Astronomical Telescopes + Instrumentation, 2008, Marseille, France

Abstract

Most computers in the past have been equipped with floating point processing capabilities, allowing an easy and brute-force solution for the machine computation errors, not requiring any specific tailoring of the computation in nearly hundred percent of situations. However, the computation needed for the adaptive optics real-time control in 30-50 meter telescopes is big enough to cause trouble to conventional von-Neumann processors, even if Moore's Law is valid for the next years. Field Programmable Gate Array (FPGAs) have been proposed as a viable alternative to cope with such computation needs^[1,2], but--at least today's chips--will require fixed-point arithmetic to be used instead. It is then important to evaluate up to what point the accuracy and stability of the control system will be affected by this limitation. This paper presents the simulation and laboratory results of the comparison between both arithmetics, specifically evaluated in an adaptive optics system. The real-time controller has been modeled as black box having as input the wavefront sensor camera digital output data, providing a digital output to the actuators of the deformable mirror, and with the task of internally computing all outputs from the inputs. MATLAB fixed-point library has been used to evaluate the effect of different precision lengths (5-10 fractional bits) in the computation of the Shack-Hartmann subaperture centroid, in comparison with the reference 64-bit floating-point arithmetic and with the noise floor of the real system, concluding that the effect of the limited precision can be overcome by adequately selecting the number of fractional bits used in the representation, and tailoring that number with the needs at every step of the algorithm.

Citation Download Citation

Yolanda Martín-Hernando, Luis Fernando Rodríguez-Ramos, and Marcos Reyes Garcia-Talavera "Fixed-point vs. floating-point arithmetic comparison for adaptive optics real-time control computation", Proc. SPIE 7015, Adaptive Optics Systems, 70152Z (10 July 2008); https://doi.org/10.1117/12.787408

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KEYWORDS

Adaptive optics

Actuators

Error analysis

Control systems

Deformable mirrors

Field programmable gate arrays

Wavefront sensors

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