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Theoretical expression for the correlation signal of nonlinear joint-transform correlators
Applied Optics
|August 25, 2010
Summary
This study introduces the nonlinear joint-transform correlator (NJTC) using a nonlinear spatial light modulator. The NJTC offers improved correlation signal construction and a derived optimal threshold for bipolar JTCs.
Area of Science:
- Optics and Photonics
- Signal Processing
- Information Technology
Background:
- Conventional joint-transform correlators (JTCs) have limitations in signal processing.
- Nonlinear spatial light modulators (SLMs) offer potential for enhanced JTC performance.
Purpose of the Study:
- To theoretically derive the correlation signal for a nonlinear joint-transform correlator (NJTC).
- To analyze the performance of NJTCs, including light utilization and bipolar JTCs.
- To determine an optimal threshold for maximizing autocorrelation peaks in bipolar JTCs.
Main Methods:
- Implementing a nonlinear spatial light modulator at the Fourier plane of a JTC.
- Modeling nonlinear effects using an error-function limiter.
- Deriving theoretical expressions for correlation signals in both linear and nonlinear JTCs.
- Analyzing the conversion of amplitude-modulated to pulse-width modulated signals in bipolar JTCs.
Main Results:
- The correlation signal of the NJTC is a convolution of the conventional signal and a nonlinear signal.
- Light utilization in NJTCs is not 100% as not all energy constructs a given correlation order.
- The bipolar JTC, using a hard limiter, converts signals to pulse-width modulation.
- An equation for an optimal threshold value, invariant to input signal separation, was obtained for bipolar JTCs.
Conclusions:
- The nonlinear joint-transform correlator provides a novel approach to optical correlation.
- The derived theoretical framework enables better understanding and optimization of NJTC performance.
- The bipolar JTC with hard limiting offers advantages in signal modulation and peak optimization.
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