Edge enhancement with incoherent optics William Stoner When this work was done, the author was located at the Raytheon Research Division, Waltham, Massachusetts 02154; he is now with RADC/ETSL, Hanscom AFB, Mas- sachusetts 01731. Received March 11, 1977. Sponsored by A. Lohmann, Universitat Erlangen- Niirnberg. A new approach to optical signal processing has recently been introduced by Gorlitz and Lanzl, 1 Lohmann, 2 and Rhodes. 3 One of the important features of the new approach, the use of a frequency offset, had been previously proposed by Macovski in a related context. 4 This Communication is a first report on independent results in this area 5 and is largely confined to experimental results, with a full account to fol- low. Operations like edge enhancement are apparently ruled out in incoherent imaging systems because of the constraints on OTFs implied by positive PSFs. The new idea is to employ a pupil plane mask in an imaging system, thereby creating a desired filter response on the unconstrained frequency offset Fig. 1. Top: if a copy of this mask is overlaid the original and shifted so the annulus is centered about the circular hole, the opaque disk in the center of the annulus is just big enough to eclipse the hole. Fig. 2. The PSF created by the pupil plane mask of Fig. 1. June 1977 / Vol. 16, No. 6 / APPLIED OPTICS 1451
Transcript
Edge enhancement with incoherent optics William Stoner
When this work was done, the author was located at the Raytheon Research Division, Waltham, Massachusetts 02154; he is now with RADC/ETSL, Hanscom AFB, Massachusetts 01731. Received March 11, 1977. Sponsored by A. Lohmann, Universitat Erlangen-Niirnberg. A new approach to optical signal processing has recently
been introduced by Gorlitz and Lanzl,1 Lohmann,2 and Rhodes.3 One of the important features of the new approach, the use of a frequency offset, had been previously proposed by Macovski in a related context.4 This Communication is a first report on independent results in this area5 and is largely confined to experimental results, with a full account to follow.
Operations like edge enhancement are apparently ruled out in incoherent imaging systems because of the constraints on OTFs implied by positive PSFs. The new idea is to employ a pupil plane mask in an imaging system, thereby creating a desired filter response on the unconstrained frequency offset
Fig. 1. Top: if a copy of this mask is overlaid the original and shifted so the annulus is centered about the circular hole, the opaque disk in
the center of the annulus is just big enough to eclipse the hole.
Fig. 2. The PSF created by the pupil plane mask of Fig. 1.
June 1977 / Vol. 16, No. 6 / APPLIED OPTICS 1451
portion of the OTF. This offset filter may be used to process a spatially incoherent, monochromatic input image, if the input image is placed on a spatial frequency carrier which matches the frequency offset chosen on the OTF.
The output image then consists of two superimposed images: a conventional, low pass filtered image; and, on a spatial frequency carrier, the image which has been filtered by the offset section of the OTF. After detection, this image is bandpass filtered and shifted to dc. To achieve this recovery of the frequency offset output image component, a sufficient frequency offset must be used. This offset can be entirely in the spatial frequency domain (as in the experimental work reported here); or it may be partially achieved in the temporal domain, by temporally modulating the phase or transmission of the pupil plane mask in an appropriate manner. In the experiments below, the input information was a transparency, (which includes the important case of radiographs), so the frequency offset was achieved by placing the transparency in contact with a Ronchi ruling. This sandwich was backlit with a diffuse mercury arc lamp, filtered for the 546.1-mμ line, to provide the necessary monochromatic and spatially incoherent illumination of the input image.
The role of the pupil plane mask, shown in Fig. 1, can be understood in the spatial domain by inspecting the PSF it creates, which is shown in Fig. 2. Fine fringes run through this PSF. These fringes shift in phase by π from one lobe to the next. If this PSF is bandpass filtered and heterodyned down to dc, a bipolar function is recovered. The over-all effect of imaging a frequency offset image with such a PSF, then bandpass filtering and heterodyning this image, is to convolve the input with the bipolar function carried by the fringes in the PSF. Since the fringes running through a PSF can be made by shift by any desired phase angle simply by choosing an appropriate phase variation on the pupil plane mask, complex valued PSFs can be implemented.
To fulfill its potential for real-time processing, the output of the incoherent processor must be coupled to a real-time bandpass filter. This may be achieved within a video chain, using the method of Schaefer and Macovski.6 Alternatively, an optically addressed coherent light modulator7-9 may be used to convert the incoherent processor output image into a modulated coherent wave so the bandpass filtering step can be performed optically. At the present time, optically addressed coherent light modulators are not readily available, and tests showed that the carrier frequency of 750 line pairs per 2.5 cm was only marginally detectable with the available high resolution video camera (a 1000-line General Electrodynamics unit). To make a demonstration of the new concept, the output of the incoherent processor was recorded on Polaroid P/N film, and the negative recording was then bandpass filtered with coherent light.
Since the OTF is given by the autocorrelation function of the pupil plane,10 the pupil plane mask shown in Fig. 1 creates an OTF with an offset region useful for suppressing frequencies about a carrier. This filter has a response about the carrier of |f | and was chosen for experimentation because it is the compensating filter used to reconstruct from projections, as is done in axial tomography.11-13 In simple terms, this filter will enhance edges. This is demonstrated by comparing Figs. 3 and 4, which show an original input pattern and the bandpass filtered image of the incoherent processor output.
Many important operations, e.g., differentiation and Fresnel transformations, are easily implemented with pupil plane masks. The Fourier transform may be also performed by adopting the Fresnel sandwich approach of Mertz.14
However, the use of incoherent processing for such nonlocal operations will be limited in space-bandwidth by the quantum
1452 APPLIED OPTICS / Vol. 16, No. 6 / June 1977
Fig. 3. A checkerboard transparency photographed at the input of the incoherent processor.
noise from a background illumination built up by the multitude of overlapping PSF images.
The author thanks George DeMars and Clarence Dunnro-wicz for fabricating pupil plane masks, and David T. Wilson for help with video and optical problems. These men are with the Raytheon Research Division, Waltham, Mass. Richard Chang, then at Johns Hopkins Hospital and now with St. Luke's Hospital Center, New York, N.Y., encouraged this work and provided a set of mammograms for experiments in the incoherent processor.
References 1. D. Gorlitz and F. Lanzl, Opt. Commun. 20, 68 (1977). 2. A. W. Lohmann, Appl. Opt. 16, 261 (1977). 3. W. T. Rhodes, Appl. Opt. 16, 265 (1977). 4. A. Macovski, Appl. Opt. 12, 1745 (1973).
5. Raytheon Research Division Reports, "A New Approach to Incoherent Optical Processing," M-2969, and "Image Processing with Incoherent Optics," M-2970 (February 1975).
6. L. Schaefer and A. Macovski, IEEE Trans. Comput. C-21, 642 (1972).
7. J. Urbach and R. Meier, Appl. Opt. 5, 666 (1966). 8. J. Feinleib and D. Oliver, Appl. Opt. 11, 2752 (1972). 9. P. Nisenson and S. Iwasa, Appl. Opt. 11, 2760 (1972).
10. E. L. O'Neill, Introduction to Statistical Optics (Addison-Wesley, Reading, Mass., 1963).
11. Z. H. Cho, IEEE Trans. Nucl. Sci. NS-21, 44 (1974). 12. T. M. Peters, IEEE Trans. Biomed. Eng. BME-19, 214 (1974). 13. S. K. Gordon and H. H. Barrett, in Image Processing for 2-D and
3-D Reconstructions from Projections, Technical Digest (OSA, Washington, D.C., 1975), p. TuC2-l.
14. L. Mertz, Transformations in Optics (Wiley, New York, 1965), p. 94.
