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Shaping the Amplitude and Phase of Laser Beams by Using a Phase-only Spatial Light Modulator

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Statistical investigation of the double random phase encoding technique.

David S Monaghan¹, Unnikrishnan Gopinathan, Guohai Situ

¹UCD Communications and Optoelectronic Research Centre, SFI-Strategic Research Cluster in Solar Energy Conversion, and School of Electrical, Electronic and Mechanical Engineering, College of Engineering, Mathematics and Physical Sciences, University College Dublin, Belfield, Dublin 4, Ireland.

Journal of the Optical Society of America. A, Optics, Image Science, and Vision

|September 2, 2009

Summary

This summary is machine-generated.

This study analyzes the amplitude-encoding double random phase encoding technique. We developed a statistical method to assess decryption key correctness, improving efficiency for large systems.

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Area of Science:

Optics
Information Theory
Cryptography

Background:

Double random phase encoding is a cryptographic technique.
Decryption key recovery is challenging for large systems.

Purpose of the Study:

To analyze the amplitude-encoding case of double random phase encoding.
To develop a statistical method for evaluating decryption key correctness.

Main Methods:

Defined a cost function (normalized root mean squared error) to quantify decryption accuracy.
Derived statistical expressions for the difference parameter (d) in the NRMS error.
Analyzed the expected value and variance of d based on output field noise characteristics.

Main Results:

The difference parameter (d) is directly related to output field noise.
Statistical expressions for d's mean and variance were derived assuming circular Gaussian noise.
Decryption error converges to statistically predicted values with increasing sample size.

Conclusions:

The derived statistical expressions provide an efficient method for key assessment in large systems.
This approach validates previous simulation results and enhances understanding of the decryption process.