Optical Correlator for Analysis of Random Fields

The invention relates generally to systems for processing optical data, and more particularly to an optical correlator for providing quantitative data on image reduction of random fields.

Motion pictures are extremely useful in obtaining information on behaviour of flow fields such as generated within a wind tunnel, propulsion system, spray, or other turbulent flow system, and which characterizes deflagrating surfaces of combusting systems. A photograph presents substantial detailed information and therefore, reduction of data contained in a movie presents a formidable data reduction problem. This problem has substantially limited the use of movies to a qualitative visual understanding of the phenomena under study. A need therefore exists for a system for reducing images of substantially quasirandom fields to quantitative data.

In the quantitative analysis of images of random fields, such as that of deflagrating solid rocket propellant surfaces, digital computer systems are generally not suitable, since digital systems handle only digital data and process data serially and relatively slowly. In particular, image analysis by a digital system requires point-by-point analog-to-digital (A/D) conversion and serial operations; the light output of the image must first be converted into digital numbers and stored, and this process repetitively performed to cover the entire image. Since the detail of a single motion picture frame may exceed 10.sup.6 pixels, the memory store for a multiplicity of frames comprising a movie is large, which may preclude use of digital analysis for data reduction of random fields.

The present invention provides an optical correlator for quantitative analysis of images of random flow fields such as those mentioned above. The invention comprises an analog optical data processing system including a series of lenses to perform optical operations on random field images under examination, and allow the examination of an entire image at once, i.e., performs parallel data processing by mapping one two dimensional data field onto another simultaneously. The correlator is simple and economical in structure and operation and has extremely fast response time, especially in data reduction of photographs or movies. A quantitative description of the correlation function of a random flow field image may be conveniently obtained.

It is therefore a principal object of the invention to provide an improved optical data correlator.

It is a further object of the invention to provide an optical data correlator for quantitative analysis of random field images.

It is another object to procide an optical data correlator for analysis of combustion systems and other turbulent flow systems.

These and other objects of the invention will become apparent as the detailed description of representative embodiments proceeds.

In accordance with the foregoing principles and objects of the invention, an optical data correlator for the analysis of images of random fields is provided which comprises a light source for projecting a beam of light along a preselected optical axis, a first lens system for receiving the beam and focusing it onto a first image, a second lens system for receiving light transmitted by the first image and focusing the light so transmitted onto a second image, a third lens system for receiving light transmitted by the second image and projecting this transmitted light onto a photodetector, and suitable electronics including an amplifier and an analog-to-digital converter for analyzing the output of the photodetector and displaying the output in useful form. Spatial filters may be included to define the projected beam, and an alignment system preferably attachable to the second image may be included to selectively position the second image.

The invention will be more clearly understood from the following detailed description of representative embodiments thereof read in conjunction with the accompanying drawings wherein:

FIG. 1 is a schematic of a representative arrangement of optical components and associated detector and data processing equipment comprising the optical correlator of the invention;

FIG. 2 is a plot of response versus frame time order in the temporal correlation of images of propellant surface burn; and

FIG. 3 is a plot of correlation function width versus frame time order in comparison of frames in a sequence of images of propellant surface burn.

Referring now to FIG. 1, shown therin is a schematic of a representative arrangement of the optical correlator system 10 of the invention. System 10 includes a light source 11 for projecting light beam 12 along an optical axis V. In a preferred embodiment, two substantially identical planoconvex lenses 14, 15 of selected diameter and focal length focus beam 12 onto a first transparency 17 disposed at the focal plane of lens 15. Suitable spatial filters 18 and 19 having appropriate aperture sizes placed substantially as shown define beam 12 and the portion thereof focused onto transparency 17. Two substantially identical chromatic imaging lenses 21, 22 of selected diametric size and focal length image light from transparency 17 onto transparency 23 disposed at the focal plane of lens 22. Alignment system 24 is operatively connected to transparency 23 to selectively position transparency 23 along axis V. Integrating objective lens system 25 projects an image of susbstantially all light transmission from transparency 23 onto photodetector 27. Photodetector 27 is operatively connected through appropriate current mode operational amplifier electronics 28 to an analog interface that includes an A/D converter 29 and microcomputer 30 so that data defining the output signal of photodetector 27 is reduced and stored in useful format.

Source 11 may be a coherent source, such as a laser, or an incoherent source, such as an incandescent lamp, light emitting diode, or the like. Comparison of the relative advantages and disadvantages of a coherent source versus an incoherent source for use in a representative system 10 built in demonstration of the invention led to the selection of an incoherent source, viz., a (500 watt) frosted incandescent bulb, because use of incoherent light minimizes interference patterns and other diffraction effects between optical components, an incoherent source is relatively inexpensive and has a signal which is linear in intensity, the frosted bulb provides uniformly diffuse illumination, light from an incoherent source is minimally affected by dust or other blemishes on the optical components, and a coherent source may require the recording of phase information whereas an incoherent source is characterized by a real wave intensity distribution.

For other than a point source 11 (i.e., an "extended" source), energy gathered by lenses 14, 15 for imaging onto transparency 17 is directly proportional to aperture size of spatial filter 18, and the flux density is inversely proportional to the square of the magnification of each lens 14, 15. Therefore, maximizing light flux density at the image plane and thereby increasing the speed of the system, make two or more lenses 14, 15 desirable, and demonstration system 10 included two identical planoconvex lenses 14, 15 each having 102 mm diameter and 165 mm focal length (combined focal length 82.5 mm), with the convex vertices in contact. The imaging lens system (21, 22) is preferably of high quality so that minute individual features on the transparencies may be correlated and, accordingly, achromatic lenses were selected and mounted in contact which reduced both spherical and chromatic aberration, preserved high resolution in the image product, and minimized interference pattern formation. Lenses 21, 22 for demonstration system 10 had focal lengths of 660 mm and 280 mm, respectively (197 mm for the combination), and diameters of 83 mm and 63 mm. Lens system 25 was selected as a multielement camera lens of focal length 31 mm and diameter 50 mm. Suitable spacings between components of system 10 were calculated based upon a 31.75 mm object size and image size corresponding to the active diameter (11.28 mm) of the photodetector. Accordingly, the spacing between aperture 18 and lenses 14, 15 was selected at 42 mm, and the spacing between transparency 23 and lens 25 was selected at 120 mm. Photodetector 27 was a planar diffused silicon PIN photodiode (1.0 cm.sup.2 active area) manufactured by United Detector Technology Inc. This detector is suited for unbiased operations (a photovoltaic mode) where the dark current and flicker noise are negligible. A Data Translation model DT2782-DI A/D converter system and MDB Systems model MLSI-1123C-R-O microcomputer were used for A/D conversion and data acquisition, handling and storage. Other commercially available components may be usable for photodetection and information processing within the scope of these teachings.

In order to derive accurate data from the analysis of images utilizing the optical correlator of the invention, it is important to accurately align the optical components, including source 11, lenses 14, 15, 21, 22, 25, and photodetector 27 along axis V. Proper alignment minimizes off-axis aberrations, interference effects, vignetting and other inaccuracies. Uniform illumination of the first transparency 17 is highly desirable and, accordingly, in the demonstration system transparency 17 was fixed at a substantially uniformly illuminated porition along axis V and transparency 23 was movable for transparency comparison in practicing the invention.

The optical correlator of the invention may be useful in the analysis of movie images of deflagrating solid propellant surfaces. Transparency alignment in such analyses is difficult since images of burning propellant surfaces lack clear definition and straight edge shapes for reference and alignment purposes. A three axis alignment system 24 was therefore incorporated into system 10 for positioning transparency 23 along axis V and in a plane perpendicular thereto, and for rotating transparency 23 about axis V.

Image analysis according to these teachings utilizes the ability of a lens to form images. With reference again to FIG. 1, if transparency 17 of transmittance f(x,y) is imaged onto transparency 23 of transmittance h(x,y), the intensity I transmitted by both is the product f(x,y)h(x,y) of the two transmittances and an output of lens system 25 and photodetector 27 may be represented as,

The analysis may be performed using either of two optical arrangements. One arrangement is that of FIG. 1 with lenses 21, 22 removed and wherein lenses 14, 15 image light onto transparencies 17, 23 disposed in contact. The intensity product of transparencies 17, 23 is integrated by lens system 25 and photodetector 27 with output defined by Eq (1). This arrangement is not desirable if one transparency is moved during use of the system because of the direct contact between the two. Therefore, system 10 described above in relation to FIG. 1 is the preferred arrangement.

Referring further to FIG. 1, by selectively moving transparency 17, transparency 23, imaging lenses 21, 22 or combination thereof, a multiplicity of one and two dimensional linear transformations may be obtained, including convolutions, correlations, power spectra, filtering, and other useful linear transformations. Consider first a one dimensional convolution and correlation. By translating transparency 23 a distance x.sub.o, photodetector 27 outputs yields a one dimensional cross correlation of the form,

A one dimensional convolution is obtained by inverting transparency 23 and shifting it a distance x.sub.o. Then,

For a two dimensional cross correlation, transparency 23 may be translated in two dimensions, yielding,

A convolution may be obtained by inverting and translating any one of the two functions. If seriatim frames of a movie are compared, a temporal as well as spatial correlation obtains.

In order to demonstrate utility of the optical correlator of the invention in the statistical analysis of random fields, fifteen different selected frames from front-lit movies of deflagrating solid propellant surfaces taken at various pressures were analyzed. A computer program used in the analyses of data is presented in Appendix A. Characteristic bright features (particle widths) at the deflagrating surface were found to vary with pressure but not with the particle mix of the propellant or with propellant type.

The transmissivity and contrast of an image of a propellant strand is not uniform across the width of the transparency and, therefore, in comparing two images, output from the photodetector indicating a condition of maximum light output does not necessarily indicate that the two images are properly aligned. To minimize background effects, a dark background and several bright features (particles) may be required for reference.

Results were significantly affected by the contrast of the transparency carrying an image of the statistical data. Therefore, in image analysis utilizing the invention, a very high contrast file was used which resulted in substantially pure black or white tones and in signal enhancement from bright intermediate sized features (particles) in the deflagration images. Sharp correlation functions providing direct measure of the sizes of bright features on the deflagrating surface were obtained from the images.

Frames of a movie were compared with respective succeeding frames to obtain a temporal as well as spatial correlation. The plot of the highest response of each frame versus the frame time order was also expected to be in the shape of an exponential decay, which would result from the decrease in particle size during burn. A damped cosine function 21 resulted, as presented in FIG. 2. The result implies that an oscillation is associated with the combustion process, and the data represents a quantitative verification of this result. A best curve fit for the data was made using a standard (chi).sup.2 fitting routine. The specified function to which the data best fit was a damped cosine curve of the form,

where A is the initial peak amplitude, B is a dc offset to the oscillation amplitude, .omega. is the oscillation frequency and .nu. is the damping rate. The optimized parameters were A=1.4, B=1.31, f=0.118, and .nu.=18.8; a 97% probability resulted that the data were nonrandom.

A similar analysis was used to measure the trend in the widths of the correlation functions versus time. FIG. 3 shows a plot 31 of cross correlation function width versus separation in time in comparing seriatim frames of a movie. Although some scatter exists in the data, the widths of the cross correlation functions increase with time between frames, which indicates movement in the apparent location of the bright features at the surface. To obtain a best data fit, a standard linear regression routine was used to make a

least squares fit to the data with a straight line,

where m is the slope and b the y intercept of the fitted line. Use of various weightings for the y values represented by the bars on the plot resulted in an output of m=4.68 and b=126.8; the probability that the data points were not correlated was only 0.4%.

The invention as herein described therefore provides a novel optical correlator for analysis of random fields, such as that of surface deflagration, wind tunnel flow, spray behavior, or other turbulent random phenomena. Modifications of the invention as described may be made, as might occur to the skilled artisan, within the scope of the appended claims, and, therefore, all embodiments comtemplated hereunder which achieve the objects of the invention have not been shown in complete detail. Other embodiments may be developed without departing from the spirit of the invention or from the scope of the appended claims. ##SPC1##