## Continuous Two-Dimensional On-Axis Optical Wavelet Transformer and Wavelet Processor with White-Light Illumination

Applied Optics, Vol. 37, Issue 8, pp. 1279-1282 (1998)

http://dx.doi.org/10.1364/AO.37.001279

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### Abstract

The wavelet transform can be expressed mathematically as a convolution between the input function and a continuous set of scaled wavelet mother functions. Optics has managed to implement only the hybrid wavelet transform in which the set of scaled wavelet mother functions is discrete but the shift is continuous. White-light illumination is used to obtain a two-dimensional, fully continuous, on-axis wavelet transformer. When the illumination source is also spatially incoherent, a complete wavelet processor may be constructed.

© 1998 Optical Society of America

**OCIS Codes**

(100.7410) Image processing : Wavelets

(110.6980) Imaging systems : Transforms

**Citation**

David Mendlovic, "Continuous Two-Dimensional On-Axis Optical Wavelet Transformer and Wavelet Processor with White-Light Illumination," Appl. Opt. **37**, 1279-1282 (1998)

http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-37-8-1279

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### References

- D. Gabor, “Theory of communication,” J. Inst. Elec. Eng. [1949–63] 93, 429–457 (1946).
- H. Szu, Y. Sheng, and J. Chen, “Wavelet transform as a bank of the matched filters,” Appl. Opt. 31, 3267–3277 (1992).
- J. M. Combes, A. Grossmann, and Ph. Tchamitchian, eds., Wavelets: Time Frequency Methods and Phase Space, 2nd ed. (Springer-Verlag, Berlin, 1990).
- X. J. Lu, A. Katz, E. G. Kanterakis, and N. P. Caviris, “Joint transform correlator that uses wavelet transforms,” Opt. Lett. 17, 1700–1703 (1992).
- J. Caulfield and H. Szu, “Parallel discrete and continuous wavelet transforms,” Opt. Eng. 31, 1835–1839 (1992).
- R. K. Martinet, J. Morlet, and A. Grossmann, “Analysis of sound patterns through wavelet transforms,” Int. J. Pattern Rec. Artif. Intell. 1(2), 273–302 (1987).
- E. Freysz, B. Pouligny, F. Argoul, and A. Arneodo, “Optical wavelet transform of fractal aggregates,” Phys. Rev. Lett. 64, 7745–7748 (1990).
- I. Daubechies, “The wavelet transform time–frequency localization and signal analysis,” IEEE Trans. Inf. Theory 36, 961–1005 (1990).
- Y. Zhang, Y. Li, E. G. Kanterakis, A. Katz, X. J. Lu, R. Tolimieri, and N. P. Caviris, “Optical realization of a wavelet transform for a one-dimensional signal,” Opt. Lett. 17, 210–212 (1992).
- Y. Sheng, D. Roberge, and H. Szu, “Optical wavelet transform,” Opt. Eng. 31, 1840–1845 (1992).
- A. W. Lohmann, B. Telfer, and H. Szu, “Casual analytical wavelet transform,” Opt. Eng. 31, 1825–1829 (1992).
- D. Mendlovic and N. Konforti, “Optical realization of the wavelet transform for two-dimensional objects,” Appl. Opt. 32, 6542–6546 (1993).
- D. Mendlovic, I. Ouzieli, I. Kiryuschev, and E. Marom, “Two-dimensional wavelet transform achieved by computer-generated multireference matched filter and Dammann grating,” Appl. Opt. 34, 8213–8219 (1995).
- A. W. Lohmann and D. Mendlovic, “Circular harmonic filters for a rotation-invariant incoherent correlator,” Appl. Opt. 31, 6187–6189 (1992).

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