Spectrally controlled interferometry

Abstract

Optical interferometers are typically categorized by their source type into incoherent (white-light) and coherent (laser). Both approaches provide adequate solutions for many measurement applications, offer unique advantages, and suffer distinct limitations. A novel interferometry method, spectrally controlled interferometry, is presented, which successfully merges many advantages from both categories while bypassing some of the limitations. The relationship between measurement accuracy and fringe stability as a function of fundamental control parameters is explored. Surface measurements of common optical components are presented, and method specific noise sources and measurement accuracy are assessed as well.

Spectrally controlled source for interferometric measurements of multiple surface cavities

“…Furthermore, fringe location and phase are both controlled electronically, removing the need for bulky and expensive translation stages dedicated to path length matching or piezoelectric transducers typically employed for phase shifting. [9][10][11] Previous methods for producing white light Fizeau interferometers have resulted in a comb-like distribution of high contrast interference fringes [12][13][14][15][16] which does not completely address the problem of fringe ambiguity and resulted in fringes would still required mechanical translation for phase shifting.…”

“…From (2) and the previous discussion of white light interferomters, the resulting coherence function is also a Gaussian function, centered at τ = 0 whose temporal width is inversely proportional to the spectral width and coherence length follows from (3). 10 g complete = g nom × m(ν; f, θ) = g nom × 1 2 + 1 2…”

Towards instantaneous spectrally controlled interferometry

“…Spectrally controlled interferometry employs the Wiener-Khinchin Theorem to produce a desirable coherence function and fringe distribution in measurement space through manipulation of the source spectral distribution in the optical frequency,ν, domain. A nominally broadband Gaussian source, g(ν; ν 0 ), centered at the mean frequency, ν 0 with bandwidth, ∆ν, is combined with a sinusoidal modulation function,m(ν; f, θ) whose control parameters: modulation frequency, f and phase, θ, have a direct relationship to producible fringe characteristics, 2 shown in Equation 1.…”

“…12 As a result of the Convolution Theorem, the final coherence function, γ SCI from Equation (1) is a combination of the nominal coherence envelope at the zero OPD location with additional copies of the nominal coherence envelopes at locations proportional to the modulation frequency, f , with an additional phase term, proportional to the phase, θ, of the modulation function, shown in Equation (2). 2 γ SCI = e −∆ντ + 1 2 e −iθ e −∆ν(τ −f ) + 1 2 e iθ e −∆ν(τ +f )…”

“…The maximum contrast of fringes in the side band coherence envelopes is limited to the 1 2 due to the normalization of the coherence function and the functional form of the modulation function. 2…”