Robust, motion-free optical characterization of samples using actively-tunable Twyman-Green interferometry

Abstract

Optical interferometry-based techniques are ubiquitous in various measurement, imaging, calibration, metrological, and astronomical applications. Repeatability, simplicity, and reliability of measurements have ensured that interferometry in its various forms remains popular-and in fact continues to grow-in almost every branch of measurement science. In this paper, we propose a novel actively-controlled optical interferometer in the Twyman-Green configuration. The active beam control within the interferometer is a result of using an actively-controlled tunable focus lens in the sample arm of the interferometer. This innovation allows us to characterize transparent samples cut in the cubical geometry without the need for bulk mechanical motion within the interferometer. Unlike thickness/refractive index measurements with conventional Twyman-Green interferometers, the actively-tunable interferometer enables bulk-motion free thickness or refractive index sample measurements. With experimental demonstrations, we show excellent results for various samples that we characterized. The elimination of bulk motion from the measurement process promises to enable miniaturization of actively-tunable Twyman-Green interferometers for various applications.

Figure 1

Balanced interferometer without a sample.

Figure 2

Rebalanced interferometer after sample insertion.

Figure 3

Change in the effective air-equivalent propagation distance $D_{\mathrm{eff}}$ before and after sample insertion and the required focal length retuning to regain interferometric balance after sample insertion.

Figure 4

Interferograms recorded by the CCD where image sets (a–c), (d–f), (g–i), and (j–l) correspond to glass samples A, B, C, and D with each respective 3-image sequence signifying TFL focal length states of $f=f_{\text{RB}}-1\text{cm}$, $f=f_{\text{RB}}$, and $f=f_{\text{RB}}+1\text{cm}$ i.e., central images (b), (e), (h), and (k) are balanced state interferograms for samples A, B, C, and D respectively.

Figure 5

CCD Interferograms for sample ’E’ (Thorlabs beam splitter cube) with TFL focal length tuned from higher to lower values and passing through the balanced interferometer configuration (in Fig.5c). Focal length values correspond to (a) $f=222\text{mm}$, (b) $f=227\text{mm}$, (c) balanced interferometer interferogram at $f=237\text{mm}$, (d) $f=247\text{mm}$, and (e) $f=252\text{mm}.$

Figure 6

The Optotune EL-16-40 TFL focal length as a function of the applied current as characterized in the lab and approximated by best fit focal length as a function of the applied current $I_{\mathrm{DC}}$ to the TFL.