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Fresnel Diffraction Sync Task

The Fresnel Diffraction sync task models near-field propagation of a complex wavefront by applying the single-FFT Fresnel transform on the GPU. For each frame, it multiplies the sampled input field \(U_0(x, y)\) by the quadratic phase factor \(\exp\!\left(i \frac{\pi}{\lambda z} (x^2 + y^2)\right)\) and performs a 2D forward FFT across the spatial axes:

\[ U_z(f_x, f_y) \propto \mathcal{F}\left\{ U_0(x, y) \cdot \exp\!\left(i \frac{\pi}{\lambda z} (x^2 + y^2)\right) \right\}. \]

The proportionality constant and output-plane chirp that appear in the analytical Fresnel integral are intentionally omitted. Positive z propagates the field forward, negative z back-propagates it.

See Wikipedia for more details on the Fresnel diffraction integral.

Warning

Set the propagation distance z to a non-zero value. A zero distance would yield an infinite phase term during lens generation, producing NaN coefficients and undefined output values.

Inputs

This task expects a single complex tensor of shape (B, H, W):

  • B: batch size (number of frames)
  • H: number of rows
  • W: number of columns

The dtype must be complex32 (CF32) and the tensor must reside in device memory.

Outputs

One output tensor is produced with the same shape (B, H, W), dtype complex32, and device memory location as the input. The data contains the Fresnel-propagated field samples at distance z up to a global complex scaling factor.

Inplace

This task has an inplace relationship between its input and output.

Ownership

This task does not own any inputs or outputs.

Settings

Example:

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{
    "lambda": 5.32e-07,
    "dx": 3.45e-06,
    "dy": 3.45e-06,
    "z": 0.1
}
Property Pattern Type Deprecated Definition Title/Description
+ lambda No number No - Wavelength in meters. Must satisfy:
- lambda > 0
+ dx No number No - Pixel pitch in meters along X. Must satisfy:
- dx > 0
- dx = dy
+ dy No number No - Pixel pitch in meters along Y. Must satisfy:
- dy > 0
- dy = dx
+ z No number No - Propagation distance in meters. Can be positive or negative.