gratingsin

Gratingsin is a term used in optics and signal-processing literature to denote a sinusoidally modulated grating pattern. The phrase is not a universally standardized term in all textbooks, but it appears in teaching materials, simulations, and some research contexts to distinguish a grating whose transmission or reflectivity varies as a sine function along one axis.

Mathematically, gratingsin is often defined as a sinusoidal amplitude or transmission pattern. A common form is G(x) = T0 [1 + m sin(2π x/Λ)], where T0 is the average transmission, Λ is the grating period, and m is the modulation depth (0 ≤ m ≤ 1). More general forms may use cosine functions or include higher harmonics. In contrast, a phase grating would modulate the optical phase rather than the amplitude. The concept can be extended to two dimensions to create sinusoidal gratings in both axes.

Optical properties and uses: When illuminated with coherent light, gratingsin patterns produce diffraction consistent with their spatial frequency content. A near-pure sinusoidal grating typically yields diffracted beams corresponding to the fundamental spatial frequency, along with the undiffracted beam, with relative intensities governed by the modulation depth and exact profile. Such patterns are useful in teaching Fourier optics, designing spatial-frequency filters, and simulating the behavior of spatial light modulators in imaging and holography contexts. They also serve as simple models for understanding how periodic modulation controls diffracted energy.

Manufacturing and variants: Sinusoidal gratings can be produced by photolithography, holographic recording, or electronically with spatial light modulators. Variants include phase gratings, which modulate phase rather than amplitude, and two-dimensional sinusoidal gratings for more complex imaging applications. The term gratingsin emphasizes the sinusoidal character of the modulation.