Signal Processing With A Nonlinear Fabry-Perot

AbstractIn this paper we consider the nonlinear Fabry -Perot and its applications to opticalsignal and image processing.*This paper addresses the signal processing aspects of a nonlinear Fabry -Perot interfer-ometer with emphasis on image processing. The device geometry is shown in Figure 1. Athin nonlinear medium, whose refractive index is a function of the light intensity insidethe Fabry -Perot is sandwiched between two plane parallel mirrors. The output as a functionof input is shown in Fig. 2, for two different values of the difference between theFabry -Perot low intensity resonance and the incident wavelength. The bistable curve in 2ais the origin of the term optical bistability and makes possible an optical memory, in whichthe output is a function of the history of the device. The Figure 2b represents a typicalnonlinear transfer curve which may be used for signal processing. It can be seen thatsmall changes in the input intensity Ic make large changes in the output intensity.The image processing function of the thin nonlinear Fabry -Perot is shown schematicallyin Fig. 3. If the Fabry -Perot is biased in the nonlinear regime, the weak inputs are onlyweakly transmitted, while slightly higher inputs are much more strongly transmitted. Thisrepresents image enhancement.The optical processing techniques available with the nonlinear Fabry -Perot are shown inFigure 4. The input is plotted as a function of t going down and the output is plotted asa function of t going left. The variable t is time, for optical signal processing anddimension along the face of the face of the Fabry- Perot, for image processing. This par-ticular representation is especially useful to demonstrate the signal processing applica-tions of the nonlinear Fabry- Perot. Differential optical gain (Figure 4a) can be used toimprove signal -to- noise, both for time -varying and spatially varying signals. This makespossible optical discrimination, background suppression, and contrast enhancement. Opticallimiting (Figure 4b), occurs because the flat output of the nonlinear Fabry -Perot asa function of input makes possible level slicing, with clipper action, and saturated output.A multistable Fabry -Perot can be achieved with higher input powers and leads to a digitaloutput for analog input. The level slicing makes possible an optical AND function, shownin Figure 5. For the two additive input signals shown, the output is large only when bothsignals are present. This makes possible an optical comparator, for either time- varyingsignals or images. Thus two images can be compared and only those features which are inboth will be transmitted.The optical memory function which is available because of the hysteresis requires acertain holding optical power. If this is available, the device retains a memory of itsprevious signal. This is useful for image retention, allowing one image to be compared toanother received later in time. Figure 6 shows how a multiple- stable -state Fabry -Perot isused to retain one image, compare it with another image occurring later in time. The de-vice retains information as to positions at with both images are bright, as well as posi-tions at which only one image is bright. The multistable Fabry -Perot is obtained bydriving the nonlinear Fabry -Perot at higher input intensities than used to achieve bistab-