Measuring a spectral bandpass of a fibre-optic spectrometer using time-domain and spectral-domain two-beam interference

Abstract

Spectral bandpasses of a miniature spectrometer with three read fibres of different core diameters are obtained using the visibility functions for both spatial and spectral fringes resolved in the interference of two light beams from a laser diode operated below the threshold. From a width of the central peak of the visibility function for the spatial interference fringes measured in the Michelson interferometer configuration with a broadband detector, the source spectral width is evaluated. From widths of the visibility functions for the spectral interference fringes measured in the Michelson interferometer configuration by the spectrometer with the different read fibres, the overall spectral bandpasses are evaluated. Subtracting the effect of the source spectral width, the spectral bandpasses of the fibre-optic spectrometer are determined. These are compared with the directly measured bandpasses using the delta-function spectrum of the same laser diode operated far above the threshold.     

High-resolution two-grating spectrometer for dual wavelength spectral imaging

A two-grating high-resolution spectrometer for dual wavelength imaging is demonstrated based on the standard Czerny-Turner mounting with an auxiliary grating and a mirror. A two-dimensional charge-coupled device (CCD) detector in the spectrometer focal plane allows simultaneous detection of two spectral intervals. Each spectrometer grating is driven by a high-precision stepper motor interfaced to a computer via home-made software. The software allows fast tuning of the gratings to a desirable spectral interval anywhere between 200 nm and 800 nm. The spectral interval widths are 2-3 nm for a 'high-resolution' (2400 grooves/mm) grating and 4-5 nm for a 'low-resolution' (1200 grooves/mm) grating. The resolution varies between 0.01 nm and 0.02 nm depending on the grating used. The performance of the spectrometer is demonstrated by detecting spectrally resolved images from a back-illuminated template and from a laser-induced plasma. The spectrometer can be useful for two-line spectroscopic diagnostics or can be expanded for multi-element spectral analysis.     

Temporal sensitivity of the wavelength calibration of a photodiode array spectrometer

Subtle differences in the relationship between wavelength and pixel on photodiode array spectrometers contribute to difficulties in transferring calibrations from one instrument to another and may even introduce errors on a single instrument over time. To quantify the level of drift that might be expected in photodiode instruments, we calibrated the wavelength scale of two Zeiss MMS-1 photodiode spectrometers weekly over a 12-month period. We found no evidence of drift in the wavelength calibration. The wavelength calibration was consistent within 0.03 nm over at least 150 days and better than 0.1 nm over the year. To provide context for the wavelength accuracy, we applied small perturbations to wavelength in two partial least squares (PLS) models. We found that wavelength perturbations introduced a linear increase in bias of about 7%/nm (for example, a 1-nm perturbation shifted fruit dry matter prediction from 14% to 21%) in a kiwifruit dry-matter model and about 3.6 °C/nm in an Intralipid temperature model. By including small wavelength perturbations in the training sets, we were able to reduce this error to less than 1.7%/nm and 0.2 °C/nm in the dry-matter and temperature models, respectively. These results suggest that the wavelength scale of photodiode instruments can be very stable. However, in light of the high sensitivity of the PLS models we examined, we recommend testing and, where possible, mitigating the sensitivity of PLS models to small wavelength shifts.     

On the spectral resolution of a focusing Bragg spectrometer

The influence of the intensity profile of a wave, focused upon backscattering from a bent crystal, on the spectral resolution of a focusing Bragg spectrometer dynamically reflecting short-wavelength X-ray radiation (λ∼1 Å) is considered in comparison to a nonfocusing flat-crystal spectrometer. Conditions necessary for resolving spectral lines in the spectrometers of both types are formulated.     

Absolute interferometric distance measurement using a FM-demodulation technique

We propose an interferometric method for measuring absolute distances larger than the wavelength. A laser diode is used as a light source. The principle of operation is based on multiple-wavelength interferometry that uses a modulated light source. This method uses the fact that the wavelength of light emitted by the laser diode can be varied by means of the injection current. The modulation of the injection current in combination with the optical heterodyne technique causes a high-frequency phase-modulated detector signal. The phase deviation of the signal is a measure of the optical path difference in the interferometer. By FM demodulation of the detector output with a phase-locked loop demodulator, the optical path difference can be determined directly without the classical ambiguity problem of interferometry. The measuring range in the experiments was limited to 50 mm by the maximum travel range of the used specimen translation stage. Because of the inherent light sensitivity of the method described, the rangefinder can be used for three-dimensional profile measurements on a wide variety of objects, even on diffuse scattering surfaces.     

White-light optical particle spectrometer for in situ measurements of condensational growth of aerosol particles

A new optical particle counter was developed to provide fast in situ sizing of cloud droplets in the Leipzig Aerosol and Cloud Interaction Simulator (LACIS). The new instrument features white light for the illumination of the sampling volume: two off-axis elliptical mirrors, providing a wide angle of collection for light scattered by particles; and an optically defined sampling volume. The smooth unambiguous response characteristic for water droplets allows direct conversion of the measured signal amplitudes into droplet diameters. Preliminary response measurements for dry polystyrol microspheres and water droplets, grown in the LACIS on NaCl particles, have shown good agreement with the corresponding calculated response curves.     

Dominant wavelength sensitivity of thin-film color filters to spectral centering

The dominant wavelength shift of 16 color filters is presented for a ±1% theoretical change in spectral centering and compared with the threshold-perceived color difference (dominant wavelength). The resulting change in dominant wavelength exceeds a threshold limit of a just-noticed color difference for some filters. Spectral-centering tolerance limits are given for the dominant wavelength to be at the threshold limit. The change in dominant wavelength is also presented from normal incidence to 60° angle of incidence, with incidence-angle limits and corresponding f-numbers for optical systems. For comparison, the color difference Δ E*(uv), from the L*u*v* color space, is calculated for each filter for ±1% spectral centering.     

Measurement of the physical properties of cyclohexane using a laser interferometric technique

A laser Mach-Zehnder interferometric modified technique providing the necessary high precision measurements of the physical properties of the most frequently used solvents for laser dyes is applied. This technique offers several advantages in the determination of the absolute value of the refractive index of cyclohexane (C₆H₁₂) at 20°C for a wavelength 632.8 nm and also its thermal coefficient. About fourteen various macroscopic and microscopic physical constants that can be derived from the refractive index are presented. In comparison with the other methods described in the literature, the accuracy and sensitivity of this technique are discussed.     

Deriving wavelength spectra from fringe images from a fixed-gap single-etalon Fabry-Perot spectrometer

A new method is described for inferring wavelength spectra from two-dimensional images of Fabry-Perot interference fringes. This new method addresses the practical difficulties that have been previously encountered in determining the fringe image's center, magnification, and distortions accurately enough to fully exploit the spectral resolution provided by the etalon. The method proceeds in two steps. First, the instrument's mapping of image position to interference order is characterized by use of images of a scene illuminated uniformly by a highly monochromatic laser. Then this information is applied to resample two-dimensional images of unknown radiation sources down to sets of one or more one-dimensional wavelength spectra. Discrete cross-correlation techniques are used at both stages of anal-     

Improvement of the oblique-incidence optical interferometric system to measure tooth flanks of involute helical gears

We put forward a plan of improving the oblique-incidence optical interferometric system applied in the measurement of tooth flanks of an involute spur gear in order to expand its capability to measure an involute helical gear. On the basis of the features of an involute helical tooth flank, we discuss how to realize the parallelism between the optical axis of the object arm of the optical system and the straight lines constructing the involute helical tooth flank. This parallelism helps the optical system produce an interference fringe pattern as clear as the one of an involute spur gear [Appl. Opt.49, 6409 (2010).]. A numerical simulation is then performed to examine the correctness of the improvement. During simulating, we unify the equation of difference tooth flanks by means of importing two parameters in relation to the left or right side of a tooth flank and the helical direction of teeth, respectively. Finally, the actual experiment is fulfilled through the real optical system built on an optical table. The simulation and experiment results verify the correctness and feasibility of the proposed improvement.     

Simple interferometric technique for generation of a radially polarized light beam

We present a theoretical and experimental investigation of an interferometric technique for converting a linearly polarized Gaussian beam into a radially polarized doughnut beam. The experimental setup accomplishes the coherent summation of two orthogonally polarized TEM01 and TEM10 beams that are obtained from the transformation of a TEM00 beam by use of a simple binary diffractive optical element. We have shown that the degree of radial polarization is maximum at a given distance from the interferometer output port that depends on the diameter of the incident beam at the interferometer input port.     

Investigation of the temperature dependence of the effective wavelength of a standard photoelectric pyrometer

A method of determining the temperature dependence of the effective wavelength of a photoelectric pyrometer, intended for standard operation in realizing a temperature scale by optical methods, is described and results are presented. __________ Translated from Izmeritel’naya Tekhnika, No. 9, pp. 52–55, September, 2007.     

Accuracy of a multiple height-transfer interferometric technique for absolute distance metrology

A multiple height-transfer interferometric technique was developed to increase the absolute distance measurement capability of a metrology system that uses a tunable laser. Using multiple accurately calibrated reference heights, this technique relaxes the requirement of knowing accurate wavelength information for multiple wavelength interferometry while maintaining its advantages. We present an uncertainty analysis, analyze the primary sources of uncertainties limiting the performance of this technique, and discuss how errors can be minimized. Measurement results of 3D images obtained from a variety of objects are presented. The measurement uncertainty is experimentally demonstrated to be 0.3?μm over 50?mm for two discontinuous surfaces with a confidence level of 95% in a lab environment.     

Interferometric measurement of the modulation transfer function of a spectrometer by using spectral modulations

We present our results on measurement of the modulation transfer function (MTF) of a given spectrometer by using the sinusoidally modulated spectrum from a Michelson interferometer with white light. We studied the MTF by varying the periodicity of the spectral fringes produced by the interferometer. Experimental data are fitted to a theoretical model to derive the spectral slit width from the measured MTF of the spectrometer.     

Application of a performance measure reduction technique to categorical safety data

This research proposes an interdisciplinary approach that combines correspondence–analytic, information–theoretic, and approximation–theoretic concepts to derive a fast reduction procedure suitable for categorical data. The procedure can also be applied to metric data where it proves to perform as well as linear regression on multivariate-normal data and superior otherwise. All types of monotone relationships, linear or non-linear, are handled well. In addition, the procedure is robust to outliers, which makes it especially desirable for exploratory and control purposes. The procedure also has a very limited data requirement, which distinguishes it from other information–theoretic procedures whose data requirement increases exponentially with the number of variables and which, in turn, are numerically highly unstable. An application of the procedure to an aviation safety data set is presented. The new procedure performs well on this data set and is shown to be analytically robust and consistent with expert judgment.     

High-accuracy spectrometer for measurement of regular spectral transmittance

A high-accuracy spectrometer has been developed for measuring regular spectral transmittance. The spectrometer is an automated, single-beam instrument that is based on a grating monochromator, reflecting optics, and an averaging sphere detector unit with a silicon photodiode. The uncertainties related to wavelength calibration, detector nonlinearity, system instability, beam displacement, polarization, stray light, interreflections, and beam uniformity are determined for the visible spectral range from 380 to 780 nm. A total uncertainty of 3 × 10(-4) (1σ) is estimated for transmittance measurements of homogeneous neutral-density filters. The uncertainty of the wavelength scale is 0.06 nm. As a specific application, calibration of V(λ)-correction filters is studied. To verify the accuracy of the transmittance measurements, a comparison of the measured and predicted transmittances of a sample of high-purity fused silica is made, revealing agreement at the 5 × 10(-4) level.