Achromatic optical elements

The principles of wavefront reconstruction by means of a geometric-optical reflection of radiation from surfaces of interference fringe maxima are discussed. The optical elements based on these principles should be achromatic. Two methods of the optical elements design are proposed. The first method is a direct holographic recording of the interference fringe structure containing only a few periods, and the second method is a combination of the measurement of the object wavefront shape with digital holography methods.     

Achromatic quarter-wave plates using the dispersion of form birefringence

We propose achromatic quarter-wave plates of a subwavelength grating structure. When the period of the grating structure is smaller than the wavelengths of the incident light, the structure is considered to be an optically anisotropic medium. The effective refractive indices strongly depend on the wavelengths, especially when the period is close to the wavelength. Using this feature, we can design a grating quarter-wave plate whose phase retardation is maintained at pi/2 for a wide wavelength range. A design method using the effective medium theory is described, and the wave plates designed were evaluated by numerical calculation with a rigorous electromagnetic grating theory. The calculation results led to the possibility of an achromatic quarter-wave plate whose retardation errors are smaller than 3 degrees for a +/-10% change in wavelength.     

White-light Phase-stepping Interferometry for Surface Profiling

Abstract

Interferometric profilers suffer from phase ambiguities if the measurement range involves a change in the optical path difference greater than a wavelength. This limitation has been overcome by using white light and scanning the object in height. We show how an achromatic phase shifter operating on the geometric phase can be used to evaluate the fringe contrast directly and to locate the position of the zero-order white-light fringe along the scanning axis.     

Achromatic system for a twisted alignment liquid crystal wavefront corrector

A twisted nematic liquid crystal wavefront corrector (TN-LCWFC) partially modulates the incident polarized light. A blazed grating may be preapplied on the TN-LCWFC to filter the unmodulated light for the purpose of stable adaptive correction. However, for broadband light, the dispersion of the blazed grating affects the image resolution. An achromatic method is presented to eliminate the dispersion of the blazed grating. Based on a prism model, we analyze the achromatic principle. An achromatic system with a conjugated blazed grating and an achromatic lens is given to eliminate the dispersion. An experiment was done with two transmitted blazed gratings so as to validate our method. Finally, a liquid crystal spatial light modulator was used as a conjugated grating to eliminate the dispersion of the blazed grating in an adaptive optics system. The results showed that the dispersion was partially compensated, and a resolvable image was achieved with a 600-700 nm wave band.     

White-light interferometry with polarization phase-shifter at the input of the interferometer

Abstract

In white-light interferometry the surface profile is determined by measuring the fringe contrast function of the white-light interferogram. One of the techniques proposed for the measurement of the fringe contrast function is the use of the phase shifting technique with the help of an achromatic phaseshifter. The available phase-shifters employ a rotating polarization component at the output end of the interferometer. Using a rotating polarization component at the input end, rather than at the output end, has certain advantages. In this paper we investigate a rotating half-wave plate phase-shifter at the input end for its applications to a white-light interferometer.     

Using minimum deviation of a secondary rainbow and its application to water analysis in a high-precision, refractive-index comparator for liquids

A new method for measuring the refractive-index difference of a liquid has been developed. The liquid to be measured is contained in a 60-mm-diameter, cylindrical glass cell, and a He-Ne laser light is passed into the cell so that the laser light incidence fulfills the condition of minimum deviation. In this condition, the beam emerging from the cell has a fine interference fringe. The position of the interference fringe is read out as a marker to measure the deflection of the laser light. Directly reading the peak shift of the interference fringe makes it easy to obtain the refractive index difference of the liquid with a fairly high precision of at least 6 x 10(-6). Further high precision is potentially expected to be realized by use of an improved data analysis treatment of the overall interference fringe pattern.     

Application of geometric phase techniques to stellar interferometry

In stellar interferometry the fringe visibility can be measured by modulating the optical path difference between the two arms of an interferometer. This approach yields accurate estimates of the fringe visibility only if the bandwidth is small, and this limits the sensitivity of the technique. We propose using a geometric phase modulator that is achromatic and does not suffer from bandwidth restrictions. Fringe detectors using geometric phase modulation have the potential of greatly increasing the sensitivity of optical stellar interferometers.     

Achromatic hybrid refractive-diffractive lens with extended depth of focus

A method for designing achromatic hybrid refractive-diffractive elements that can produce beams with long focal depths while they preserve the entire aperture for capture of light and high transverse resolution is presented. Its working principle is based on the combination of a diffractive optical element that generates a long range of pseudonondiffractive rays and a refractive lens of opposite dispersion to form an achromatic hybrid lens. A hybrid lens with a fast f-number (f/1) that works in the entire visible wave band (400-700 nm) was designed and fabricated. Simulation results demonstrate a factor-of-10 improvement in depth of focus compared with that of a conventional f/1 lens, with matching 1-microm lateral resolution. Experimental results confirm the effectiveness of the proposed method through demonstration of an achromatic hybrid lens with better than a factor-of-7 improvement in depth of focus and 1-microm transverse resolution.     

Interpretation of interferograms in studies of gaseous impurity concentration

Relations are given for interpreting interferograms in terms of concentrations. The correction for achromatic fringe displacement is given for an air-carbon dioxide mixture determined on an IZK-454 interferometer.     

Full-field optical coherence tomography by achromatic phase shifting with a rotating polarizer

We demonstrate two-dimensional detection optical coherence tomography (OCT) using achromatic phase shifting with a rotating polarizer. This phase shifting, which experiences a light beam with a cyclic change in its polarization state, is, in principle, independent of wavelength. We simulated the wavelength dependence of an achromatic phase shifter using Jones calculus and found that the achromatic region exceeded 145 nm when the deviation of the phase retardation was less than +/- 0.5 degrees. Using the achromatic phase shifter and a conventional phase-shift calculation method, we obtained en face OCT images of an onion at different depths. This method is effective to enhance the quality of OCT with an ultrabroad-spectrum light source.     

A New Method for Spectral Performance Evaluation of a Chromatic and Achromatic Quarter-Wave Retarder

When a polarized polychromatic beam passes through a quarter-wave retarder, the constituent spectral components suffer different changes in the state of polarization. As a result, when the beam passes through an analyzer, the intensity of the resultant beam changes, depending on the orientation of the analyzer, state of polarization of the input beam, spectral and spatial intensity distribution of the source and the wavelength-dependent retardance of the quarter-wave retarder. The intensity variation of the resulting beam is theoretically and experimentally observed, with the variation of the azimuthal angle of the analyzer for film-type chromatic and prism-type achromatic quarter-wave retarders. The spectral performances of achromatic retarders are generally evaluated by measuring retardances at discrete wavelengths by using a monochromatic beam of light over the wavelength range of interest. In this study, a simple method is used for computing the fractional nonlinear polarization (FNLP) from theoretically and experimentally obtained intensity variations for evaluating the spectral performance of both achromatic and chromatic quarter-wave retarders operating over a broad spectral range in the visible region using a polychromatic beam of light. FNLP variation is also shown for a film-type chromatic quarter-wave retarder using a monochromatic source of light. The experimentally obtained values are compared with theoretical values and a good agreement is observed. The applications of the method for the performance evaluation of quarter-wave retarders are discussed.     

Coherence confocal-imaging system for enhanced depth discrimination in transmitted light

A system for image-plane holography that uses a spectrally and spatially broad radiation source is analyzed and shown to provide depth discrimination in excess of that offered by conventional confocal imaging. The enhanced depth discrimination is a consequence of two factors: the simultaneous reduction of both the spatial and the temporal coherence of the source, and the special property of certain grating interferometers of presenting a spectrally dispersed light beam to the object while forming achromatic fringes at the hologram-recording plane.     

Efficient polarization converter for projection displays

In the waveguiding limit, a twisted nematic liquid crystal cell behaves as an achromatic polarization rotator. We propose and demonstrate the application of such a polarization rotator to convert unpolarized light into linearly polarized light with almost 100% efficiency. This polarization converter has a 2:1 aspect ratio, which is close to the 16:9 ratio for modern televisions. It can be used therefore in a projection display with polarization-dependent light valves such as a liquid crystal light valve. Both transmittive and reflective light valves can be used. The temperature dependence of the achromatic polarization rotator is also studied.     

Optimal design of achromatic true zero-order waveplates using twisted nematic liquid crystal

Phase retarders usually show strong wavelength dependence. A novel and simple configuration with the combination of two twisted nematic liquid-crystal cells is proposed for the design of a true zero-order achromatic quarter-wave plate. The present optimization method considers the material dispersion. Simulation computations show a good achromatic behavior of the optimized waveplate. Compared with other types of broadband quarter-wave plates, the present device is compatible with classical liquid-crystal displays and can be expected to be used in precision polarimeters with low cost and enhanced light efficiency.     

Scale-tunable optical correlation with natural light

We describe two different scale-tunable optical correlators working under totally incoherent light. They behave as spatially incoherent wavelength-independent imaging systems with an achromatic point-spread function (PSF). In both cases it is possible to adapt the scale of the achromatic PSF, i.e., to modify the scaling factor of the PSF and preserve the chromatic compensation, by one's shifting the input along the optical axis. The remarkable properties of these systems allow us to carry out a scale-tunable color pattern-recognition experiment with natural light.     

Design of a static Fourier-transform spectrometer with increased field of view

We present several novel designs of static Fourier-transform spectrometers based on Wollaston prisms. By numerical modeling we show the increased field of view that can be obtained when an achromatic half-wave plate is included between the prisms or when prisms fabricated from positive and negative birefringent materials are combined. In addition, we model how a single Wollaston prism with an inclined optic axis produces a fringe plane localized behind its exit face, thus enabling the design of a static Fourier-transform spectrometer based on a single Wollaston prism.     

Photon-noise limits to the detection of the closure phase in optical interferometry

Michelson stellar interferometers with long baselines have been proposed as a means for obtaining high-resolution images of space objects. The fringes measured in such interferometers move randomly owing to atmospheric turbulence effects. For overcoming turbulence effects the fringe phase at any instant is summed around groups of three or more aperture pairs to create the so-called closure phase. The closure phase is insensitive to atmospheric turbulence effects; however, it is corrupted by photon-noise effects. The probability-density function of the error in the closure-phase estimate that is due to photon noise is derived as a function of the fringe visibility and is evaluated. It is shown that, for dim objects and low fringe visibility, several hundred to several thousand independent realizations of the closure phase must be averaged to obtain acceptable closure-phase variance.     

Single-shot color fringe projection for three-dimensional shape measurement of objects with discontinuities

A simple but effective fringe projection profilometry is proposed to measure 3D shape by using one snapshot color sinusoidal fringe pattern. One color fringe pattern encoded with a sinusoidal fringe (as red component) and one uniform intensity pattern (as blue component) is projected by a digital video projector, and the deformed fringe pattern is recorded by a color CCD camera. The captured color fringe pattern is separated into its RGB components and division operation is applied to red and blue channels to reduce the variable reflection intensity. Shape information of the tested object is decoded by applying an arcsine algorithm on the normalized fringe pattern with subpixel resolution. In the case of fringe discontinuities caused by height steps, or spatially isolated surfaces, the separated blue component is binarized and used for correcting the phase demodulation. A simple and robust method is also introduced to compensate for nonlinear intensity response of the digital video projector. The experimental results demonstrate the validity of the proposed method.     

Robust determination of optical path difference: fringe tracking at the infrared optical telescope array interferometer

We describe the fringe-packet tracking system used to equalize the optical path lengths at the Infrared Optical Telescope Array interferometer. The measurement of closure phases requires obtaining fringes on three baselines simultaneously. This is accomplished by use of an algorithm based on double Fourier interferometry for obtaining the wavelength-dependent phase of the fringes and a group-delay tracking algorithm for determining the position of the fringe packet. A comparison of data acquired with and without the fringe-packet tracker shows a factor of approximately 3 reduction of the error in the closure-phase measurement. The fringe-packet tracker has been able so far to track fringes with signal-to-noise ratios as low as 1.8 for stars as faint as mH = 7.0.     

Actively recording the average shift of the achromatic band in white-light interferometers

Measurement of the refractive index of a substance in a strong turbulent gas flow is described. An adaptive photoelectronic unit is proposed for determining the average position of the achromatic fringe when the light-wave phase, recorded by the photodetectors of a white-light interferometer. Translated from Izmeritel'naya Tekhnika, No. 10, pp. 38–42, October, 1996.