apodisation

Apodisation is the deliberate smoothing of a function near its boundaries by applying a tapering, or apodizing, profile. In practice this means gradually reducing the transmission across an optical aperture or weighting a finite-duration signal toward its edges to suppress edge effects.

In optical systems, apodisation multiplies the complex pupil field by a real-valued transmission function A(r) that falls from near unity at the center to lower values at the edge. The resulting point spread function has lower sidelobes, improving contrast and suppressing diffraction rings. The trade-off is lower throughput and broader main lobe, reducing resolution or peak intensity. Common profiles include Gaussian, cosine, and polynomial tapers; shaped-pupil and Phase-Induced Amplitude Apodization (PIAA) are more advanced methods.

In digital signal processing, apodization refers to windowing the time-domain signal with a weight function w(n). This reduces spectral leakage when computing the discrete Fourier transform. Popular windows include Hann (Hanning), Hamming, Blackman, and Kaiser, each with different sidelobe suppression and main-lobe width.

Applications of apodisation span astronomical imaging, laser beam shaping, spectroscopy, and ultrasound, as well as measurement systems where reducing edge artifacts is beneficial. The choice of apodization profile involves trade-offs between throughput, resolution, and sidelobe suppression.