A uniqueness theorem is proven for the problem of the recovery of a complex valued compactly supported 2-D function from the modulus of its Fourier transform. An application to the phase problem in optics is discussed.

The fractional cosine and sine transforms – closely related to the fractional Fourier transform, which is now actively used in optics and signal processing – are introduced and their main properties and possible applications are discussed.

The sampling theory is basic and crucial in engineering sciences. On the other hand, the linear canonical transform (LCT) is also of great power in optics, filter design, radar system analysis and pattern recognition, etc. The Fourier transform (FT), the fractional Fourier transform (FRFT), Fresnel transform (FRT) and scaling operations are considered as special cases of the LCT. In this paper,...

It has been shown that the fractional Fourier transform, recently very intensively investigated in mathematics, quantum mechanics, optics and signal processing, can be obtained as a special case of the earlier introduced linear coordinate transformations of the ambiguity function or Wigner distribution. Some applications of the generalized fractional transform on the time-frequency analysis are...

The fractional cosine and sine transforms – closely related to the fractional Fourier transform, which is now actively used in optics and signal processing, and to the fractional Hartley transform – are introduced and their main properties and possible applications as elementary fractional transforms of causal signals are discussed.

Wave-front reconstruction with the use of the fast Fourier transform (FFT) and spatial filtering is shown to be computationally tractable and sufficiently accurate for use in large Shack-Hartmann-based adaptive optics systems (up to at least 10,000 actuators). This method is significantly faster than, and can have noise propagation comparable with that of, traditional vector-matrix-multiply rec...

The two main approaches for the description of sound fields are methods derived from solutions of the wave equation and geometric methods based on analogies to ray optics. Their mathematical representations are reviewed and it is shown that representations by projective geometry and descriptions by Fourier acoustics lead to similar parametric representations of sound fields.

The design of Agilent Cary 600 FTIR Series spectrometers focuses on performance. This is achieved through innovative optics design, with an emphasis on optical throughput. The result is an FTIR series that offers unrivalled sensitivity and performance. A larger footprint is required, but this is a negligible compromise for the customer, given the vast increase in productivity and profitability ...

The spatial organization of stromal collagen of ex-vivo corneas has been quantified in adaptive-optics second harmonic generation (SHG) images by means of an optimized Fourier transform (FT) based analysis. At a particular depth location, adjacent lamellae often present similar orientations and run parallel to the corneal surface. However this pattern might be combined with interweaved collagen...

The original definition of the derivatives of a function makes sense only for integral orders, i.e. we can speak of the first or second derivative and so on. However, it is possible to extend the definition of the derivative to noninteger orders by using an elementary property of Fourier transforms. Bracewell shows how fractional derivatives can be used to characterize the discontinuities of ce...