Analysis of compressive sensing with optical mixing
using a spatial light modulator
Zhijing Zhu, Hao Chi,* Shilie Zheng, Tao Jin, Xiaofeng Jin, and Xianmin Zhang
Department of Information Science and Electronic Engineering, Zhejiang University,
38 Zheda Road, Hangzhou 310027, China
*Corresponding author: chihao@zju.edu.cn
Received 22 December 2014; revised 28 January 2015; accepted 28 January 2015;
posted 29 January 2015 (Doc. ID 231211); published 3 March 2015
Compressive sensing (CS) in a photonic link has a high potential for acquisition of wideband sparse sig-
nals. In CS it is necessary to mix the input sparse signal with a pseudorandom sequence prior to sub-
sampling. A pulse shaper with a spatial light modulator (SLM) can be used in photonic CS as an optical
mixer to improve the speed of mixing. In this approach, the sparse signal is modulated on a chirped
optical pulse and the pseudorandom sequence is recorded on the SLM within the pulse shaper. The op-
tical mixing in the frequency domain is realized based on the principle of frequency-to-time mapping. In
this paper, we investigate the performance and limitations of photonic CS with an SLM in detail. A theo-
retical model to describe optical mixing based on frequency-to-time mapping is presented. We point out
that there is an upper limit on the length of the pseudorandom sequence recorded on the SLM that can be
mixed with the sparse signal due to the condition of the far-field approximation of the frequency-to-time
mapping. Since the length of the pseudorandom sequence is one of the major factors that affect the signal
recovery performance in CS, this limitation should be fully considered in the system design of the CS with
optical mixing in the frequency domain. We present numerical and experimental results to verify
the theoretical findings. Discussion on the performance improvement is also presented. © 2015 Optical
Society of America
OCIS codes: (320.7085) Ultrafast information processing; (250.4745) Optical processing devices.
http://dx.doi.org/10.1364/AO.54.001894
1. Introduction
The Shannon/Nyquist sampling theorem is one of the
foundations of modern signal processing [
1]. Nowa-
days, the improvement of analog-to-digital convert-
ers lags far behind digital signal processing, which
is mainly due to the lack of an ultrafast sampling
clock with low timing jitter. Recently developed com-
pressive sensing (CS) provides a potential way to
overstep the limitation of the sampling rate, by
which a wideband sparse signal can be captured with
measurements well below the number expected from
the Shannon/Nyquist theorem. The sparse signal re-
fers to any signal that is sparse in a certain orthogo-
nal basis. The process of a CS system includes a
measurement process and a reconstruction process.
The measurement process involves the mixing of
the sparse signal with a pseudorandom sequence,
low-pass filtering, and sub-Nyquist sampling. In
the reconstruction process the input sparse signal
is recovered at or above the Nyquist rate from the
measurement results with a recovery algori thm.
The random demodulator and modulated wideband
converter (MWC) are two well-developed CS tech-
niques for acquisition of wideband sparse signals
[
2–14].
Recently, implementation of CS with photonic
techniques has attracted lots of research interest,
since it offers higher bandwidth by moving the oper-
ations of modulation, mixing, and filtering into the
optical domain [
2–15]. At this point, several photonic
CS schemes have been proposed. Experimental
realization of CS in a photonic link was also
1559-128X/15/081894-06$15.00/0
© 2015 Optical Society of America
1894 APPLIED OPTICS / Vol. 54, No. 8 / 10 March 2015