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We propose a model for coherence scanning interferometry using familiar Fourier optics methods and the spectrum of plane waves for the case where light source spectral bandwidth limits the fringe contrast as a function of optical path length. The model is straightforward to implement, is computationally efficient, and reveals many of the common error sources related to the optical filtering properties of the imaging system. We quantify the limits of applicability of the model related to the geometrical approximations for Fourier optics, particularly for high numerical apertures, and when using the fringe contrast for determining surface heights. These limitations can be overcome using a three-dimensional imaging model.

In retinal optical coherence tomography (OCT), it is significant to focus the scan beam on the retina layers of the human eye fast to acquire high-quality OCT images. The refractive errors of the human eye are usually compensated by shifting the optical lens in the sample arm manually or electrically. Otherwise, refractive errors of the human eye will cause axial focal shift of the scanning beam and blur the OCT images. We propose a fast automatic focus method using the interference fringes magnitudes of the whole retinal layers to determine the best refractive correction position of motor-driven optical compensation lens without the aid of optical fundus imaging or OCT B-scan imaging. Also, the optical path difference between the sample arm and reference arm is adjusted in the spectral-domain OCT (SD-OCT) to reduce the effects of sensitivity roll-off. The experiments in the lab-built SD-OCT show that the average running time of the method is 15.2 s and the mean absolute deviation of each imaging is within 1 mm. The method is independent of extra optical setup and requires less computational consumption, which is suitable for low-cost and automatic retinal OCT devices.

The possibility of using the phase of second-harmonic interference fringes as a position marker for detecting the zero optical path difference (OPD) in a nonlinear pulse-train interferometer is investigated. A theoretical analysis showed that the phase of second-harmonic fringes can be used as a position marker for detecting the zero OPD, and compared to the phase of the fundamental wave, it provides a higher coefficient of sensitivity to the change in distance. In a nonlinear pulse-train interferometer, the phases of the fundamental and second-harmonic fringes were measured, and the positions of their zero-crossing points near the fringe envelope peak were compared. A difference between these two positions and the effectiveness of the proposed method were confirmed. The concept and analysis reported herein pave the way for the development of higher-accuracy, absolute distance measurements.

The availability and reliability of the high data rate space-to-ground optical coherent communication links are critically challenged because the wave front of the signal beam is distorted and impaired when propagating through atmospheric turbulence. Based on the free-space interference of two successive data bits delayed by an unequal-arm-length Mach–Zehnder interferometer (MZI), a pupil-matching time-delay self-homodyne interference differential phase-shift keying (DPSK) optical receiver with 2 × 4 90-deg optical hybrid is designed for the high data rate space-to-ground optical communication links due to its immunity from wave front impairment. The delayed optical path difference (OPD) in the unequal-arm-length MZI corresponds to the duration of one bit and can be stabilized to below 1000th of the wavelength by the closed-loop feedback control. The maximum system insertion loss is

In a pulse-train interferometer, the position of zero optical path difference (OPD) between the reference and object mirror can be obtained using the envelope peak of the interference fringe signal. Based on communication theory, frequency/phase information can provide higher accuracy compared to envelope/amplitude information. We propose a phase information-assisted method to obtain the position of zero OPD for a pulse-train interferometer. We demonstrate and verify that this phase approach can be used to determine the position of zero OPD with high accuracy using experimental data. This method is reliable and provides good performance for length measurement.

A method of eliminating echelle mosaicking errors using a single-interferometer system combined with a mirror-echelle structure and double-angle incident light is proposed. Coplanar and in-plane mosaicking errors are, respectively, removed using interference fringes at zero order and diffraction order, and double-angle incidence light is exploited to erase the longitudinal offset. Two mirror-echelle structures, both with aluminum reserved for a mirror on the echelle plane to receive the double-angle incident light, are designed. The relationship between mosaicking error and the optical path difference is established. The evolution of the interference fringe pattern of mosaicking process is simulated, and a mosaicking experiment is then conducted following the simulation.

A silicon microresonator consisting of an asymmetric embedded dual microring (EDMR) with a U-bend feedback coupled waveguide (FCW) is proposed and investigated for possible applications in sensing. A Fano resonance originates from the optical interference between the EDMR and racetrack-like resonator (RTR) in the proposed device. The interference between a high-Q EDMR cavity and a low-Q RTR cavity can increase the extinction ratio (ER) of Fano spectrum. The slope of Fano resonance can be well tuned by changing loss factor β of FCW. We can see the periodic spectrum transits from Lorentz profile to Fano profile by changing optical path length L of FCW. The maximum ER of Fano resonance is as high as −45 dB. Our sensor exhibits sensitivity of 1.2 × 104 dB / nm, and a minimum detection limit of 2 × 10 − 7 RIU. Moreover, for such a structure, the fabrication is simple and CMOS compatible. The sensor’s performance is simulated for ethylene glycol (C2H6O2) solution. The microcavity with optimized geometric structures presented provides the potential for ultracompact sensing applications.

An implementation of a distance measurement system using double-sideband with suppressed carrier modulation (DSB-SC) frequency scanning interferometry is proposed to reduce the variations in the optical path and improve the measurement accuracy. In this proposed system, the electro-optic DSB-SC is used to create dual-swept signals with opposite scanning directions. For each swept signal, the relative distance between the reference arm and the measuring arm is determined by the beat frequency of signals from two arms. By multiplying both beat signals, measurement errors caused by variations in the optical path can be greatly reduced. As an experimental demonstration, a vibration was introduced in the optical path length. The experimental results show that the variations can be suppressed for over 19.9 dB.

We proposed an optical sensing scheme, based on the mechanism of weak measurement, to detect the sonic pressure transversally without any disturbance. According to the theory of weak measurement in frequency domain, a tiny phase difference between the two eigenstates of the system could be detected, depending on the shift of central wavelength of output spectra. The optical path difference between two paths of a Mach–Zehnder interferometer is induced by the varied acoustic waves propagating in liquid. The propagating direction of the testing light beam is orthogonal to that of the acoustic wave. Thus, the phase shift corresponding to the changing acoustic pressure could be monitored transversally. The experiment with the hydrophone is implemented as a reference to demonstrate the feasibility and authenticity of this weak measurement scheme. With this method, an optical phase resolution of 1.12×10−5 rad was acquired in such a weak measurement system.

Using additive manufacturing techniques in optical engineering to construct a gradient index (GRIN) optic may overcome a number of limitations of GRIN technology. Such techniques are maturing quickly, yielding additional design degrees of freedom for the engineer. How best to employ these degrees of freedom is not completely clear at this time. This paper describes a preliminary design philosophy, including assumptions, pertaining to a particular printing technique for GRIN optics. It includes an analysis based on simulation and initial component measurement.

We have proposed and experimentally demonstrated a fiber-optic temperature sensing system based on an optoelectronic oscillator (OEO). A part of the fiber in the oscillator loop is used as the sensing fiber. As the free spectrum range (FSR) of the OEO is determined by the length of the oscillator loop, when the temperature of the sensing fiber is changed, the refractive index of the fiber varies; thus, the optical path length changes as well as the FSR of the OEO. By tracking one peak of the OEO harmonics, the temperature variation can be monitored. Therefore, the temperature variation can be converted to the frequency shift of the radio frequency signals. In the experiment, we have measured the spectra of the OEO with different temperatures, which show good sensing linearity. We have also measured the relationship between the sensing responsivity and the tracked frequency (1.0, 1.5, 2.0, and 3.0 GHz) in the experiment, which shows that the harmonics at a higher frequency produce a higher sensing responsivity. The proposed temperature sensing system exhibits good tunability, stability, linearity tailorable sensing responsivity, and ease of implementation, thus it shows good application potential in remote fiber-optical temperature sensing and monitoring.

A differential interferometric technique for the measurement of surface roughness of plane optical surfaces is proposed. A polarization Sagnac interferometer, placed in the image space of a reflection microscope system with linearly polarized, spatially coherent, quasimonochromatic incident beam illumination, splits the image-forming beam from a plane test surface (TS) into laterally sheared (LS) linear orthogonal components. The LS components interfere when brought to the same state of polarization. The optical path difference (OPD) variation along the direction of lateral shear is a measure of the slope variation on the TS. Polarization phase shifting interferometry has been applied to extract the OPD variation and thus the slope distribution, slope errors, and, subsequently, height errors. System error contribution is eliminated by combining height error data obtained for parallel sections of the TS that lie along a section of the image field parallel to the direction of lateral shear, as the TS is shifted in a direction normal to the lateral shear direction between the data capture. Results obtained for an aluminized plane polished TS are presented.

When the optical path difference between the two arms of an interferometer is so small that only one peak exists within the measurable interference spectrum, traditional white light interference demodulation tech- niques based on two adjacent interference peaks are not a suitable choice. We report an experimental approach to measure the peak wavelength shifts with only a single interference peak in a fiber white light interferometer. The temperature measurement experiments prove a linear relationship between the peak wavelength and the

A sinusoidal wavelength scanning interferometer with the four-step phase-shift method is demonstrated for a three-dimensional profile measurement. The interference phase-shift signal generated by the sinusoidal wavelength scanning contains information about optical path difference covering a nm-μm scale structure. The interference phase-shift signal was obtained by the four-step phase-shifting method. The sinusoidal wavelength shifting with a frequency of approximately 180 Hz and tunable range of 5.7 nm was performed by the Littman–Metcalf external resonator-type tunable laser with a center of 772.1 nm. The full-field surface profile measurement was conducted by a charge coupled device image sensor with an accuracy on a nm scale. The surface profiles of gauge blocks with a step height up to about 10 μm were successfully measured with a surface profile irregularity of 3.8×10−2 μm. The deviations of two measured surfaces of upper and lower steps were estimated to be 1.6×10−2 μm and 3.1×10−2 μm, respectively.

A simple and effective automatic positioning method (APM) is proposed for the application of annular subaperture stitching interferometry in the stage of precision polishing. In the testing process, a series of optical path difference (OPD) data of subaperture are obtained since the interferometer is shifted relative to the tested aspheric surface. These OPD data are analyzed by the APM to get the key stitching parameters (e.g., aspheric departure) without a precision motion system. The basic principles of the APM are described. The performance of the method is simulated in some pertinent cases. Finally, we study the applicability of the proposed method to subaperture stitching tests of a hyperbolic mirror. The stitching results agree with the full-aperture test results. It demonstrates the validity and practicability of the proposed algorithm.

An improved structure for the optical coherence tomography (OCT) scheme based on a 4×4 fiber coupler for simultaneously measuring the refractive index and thickness of optical samples is presented. The proposed structure incorporates the optical path length difference of interference light and is used to calculate the refractive index and thickness of an unknown sample without any prior knowledge of the sample parameters. Two methods (time-domain and Fourier-domain OCT) of obtaining information about an unknown sample are proposed, and a high-speed high-resolution OCT system was developed.

Laser gated viewing is a prominent sensing technology for optical imaging in harsh environments and can be applied for vision through fog, smoke, and other degraded environmental conditions as well as for the vision through sea water in submarine operation. A direct imaging of nonscattered photons (or ballistic photons) is limited in range and performance by the free optical path length, i.e., the length in which a photon can propagate without interaction with scattering particles or object surfaces. The imaging and analysis of scattered photons can overcome these classical limitations and it is possible to realize a nonline-of-sight imaging. The spatial and temporal distributions of scattered photons can be analyzed by means of computational optics and their information of the scenario can be restored. In particular, the information outside the line of sight or outside the visibility range is of high interest. We demonstrate nonline-of-sight imaging with a laser gated viewing system and different illumination concepts (point and surface scattering sources).

In designing the optics of an imaging multi-etalon spectro polarimeter as a post-focus instrument for the Advanced Technology Solar Telescope (ATST), many constraints must be considered. Among these are the large entrance pupil diameter of the telescope (4 m), the demanded large field of view (>= 90 arc sec), high spectral resolving power (>= 200; 000), and limited field-dependent blue-shift of the instrumental profile [= 200 mm), lighted by highly collimated beams. This implies large optical elements and long optical paths. Moreover, to use interference pre-filters with a relatively small diameter (

A high-efficiency tunable refractive lens based on liquid crystals with concentric electrode rings and a simple unique design of a resistor network is reported, and used to assess the performance of an optimized electrically tunable lens. It has a large number of phase control points to be able to accurately control the phase profile and produce high efficiency. The lens design uses resistors between neighboring electrodes to minimize external connections. The lens optical path difference is measured as a near perfect parabolic shape and the Strehl ratio of about 80% is obtained (comparing to a high-quality glass lens). Image evaluations show a good image quality with diffraction limited resolution, but the contrast is lowered by a large-area haze. The lens design also shows a good switching speed, and adjustable power, allowing it to be used in many applications. An example lens with a diameter of 2.4 mm and a 5 diopter tunable range is used in the evaluations.

Numerical databases established by large-eddy simulations of subsonic turbulent boundary layers and separated shear layers are utilized to simulate Malley probe measurements and investigate their accuracy and consistency with the data obtained from two-dimensional (2-D) wavefront sensors. It is found that the Malley probe data give a good approximation for the boundary layer and a reasonable approximation for the separated shear layer in terms of the root mean square of optical path difference (OPD rms ) and the streamwise correlations of OPD. The OPD rms from the Malley probe is slightly smaller than that from the 2-D wavefront sensor with the same streamwise aperture size for both flows. It is shown that the use of multiple Malley probes in the transverse direction of the flow can enhance the accuracy of measurements. The spatial correlations of OPD obtained from simulated multi-Malley-probe data are also examined and compared to those from 2-D wavefront sensors.

With the current retinal imaging systems, laser cavities and astronomical spectroscopes, there is the need to employ off-axis reflective systems. These systems, often used in configurations where the object or image are at the infinite with respect to the spherical mirrors, are the most used in this type of instrumentation. Expressions for the wavefront aberrations in an off-axis spherical mirror with image or object at the infinite are presented, analyzed and evaluated. Formulas are derived from the optical path difference between a paroboloid, as reference surface, and a sphere. Exact and approximate expressions, assuming a relative small pupil and a small angle of incidence are presented. They can be used to design and analyze some off-axis reflective systems.

A simple, new, self-referenced technique for the internal measurement of a right angle is presented. A polarization cyclic path optical configuration (CPOC) receives as the input beam a pair of laterally separated plane wave components, having angular separation of ψw = (π±4nδ), produced due to internal reflection of a linearly polarized plane wave on the surfaces enclosing the 90-deg (±δ) angle of a right-angled prism (where δ is the error in 90-deg angle and n is the index of refraction of the material of the prism). The CPOC is used to superpose the mutually inclined plane wave components by duplicating the input pair of plane wave fronts and introducing appropriate lateral shear between the identical pairs. The superposed inclined plane wave components interfere to produce two beam Fizeau fringes (FF), when brought to the same state of polarization. The error in the right angle can be calculated simply from the spacing of the resulting FFs or, more accurately, from the slope of the optical path difference variation obtained by applying polarization phase-shifting interferometry. Results obtained for a right-angled prism are presented.

When an optically guided hypersonic vehicle flies in the atmosphere, the scene is viewed through an optical dome. Because of hypersonic friction with the atmosphere, the optical dome is inevitably covered by a serious shock wave, which threatens to alter the dome's physical parameters and further induce wavefront distortion and degradation of images. By studying the physical phenomena occurring within the optical dome in such an adverse environment, this paper identifies the relationship between the variation of the dome's optical characteristics and the infrared image degradation. The research indicates that the image quality degrades sharply as the vehicle's Mach number increases. Simulations also show that while the thermo-optic effect, elastic-optic effect, thermal deformation, and variation of transmittance have little effect on the optical system, the thermal radiation severely degrades images when vehicles fly at hypersonic speeds

Herein, we sincerely make an apology to readers for our misguidance. We have made a mistake on the analysis of the optical path difference produced by the Savart polariscope which resulted in the improper design of a wide-field-of-view Savart polariscope. The correct statements are presented.

As a measuring technique, owing to its high throughput and multichannel advantages, interference imaging spectroscopy is widely used in many fields. This technique can be classified as temporally modulated Fourier transform spectrometer (TMFTS) and spatially modulated Fourier transform spectrometer (SMFTS). In contrast to TMFTS-based instruments, instruments using SMFTS are more stable, simple, and compact. In spectrometry, improvements of the spectral resolution and the optical throughput are always the focus points. A new static Fourier-transform imaging spectrometer based on the use of Wollaston prisms is presented. The novelty of this work comes from the use of a longer optical path difference, which provides higher spectral resolution. The principle and the system configuration are described. An experimental system based on the Wollaston prisms has been built and preliminary imaging spectroscopy experiments have been performed with it.

Frequency sweeping interferometry (FSI) is a technique where absolute distance measurements are made without ambiguity, using synthetic wavelengths resulting from frequency sweeps. Accuracy is mainly dependent on the synthetic wavelength measurement using a Fabry-Perot interferometer to count resonances as frequency sweeps. Measurement uncertainty increases with distance due to propagation of uncertainty in the synthetic wavelength measurement. For large distances, the number of fringes dominates performance, leading to a linear decrease of accuracy with range. To overcome this problem, the dual FSI concept was introduced, where the measurement process for large distances is reduced to the close-range case, by limiting the interferometer optical path difference. This is achieved by increasing the reference arm with a long reference fiber, and using an ancillary interferometer to calibrate the fiber length continuously. This dual FSI concept was implemented and fully tested in view of ESA-PROBA3 space mission. The sensor is composed of an external cavity diode laser, a high-finesse Fabry-Perot interferometer, and a dual measurement system. Accuracies better than 32 µm for a measurement range from 51 to 61 m were achieved using a reference fiber with 71 m, while maintaining the reduced complexity inherent to FSI technique, which is mandatory for space applications.

In thin-film silicon solar cells, a flexible optical design for light collection is developed that can lead to zero reflection loss and enhance the optical path length in the absorber layer. In this work, we demon- strate two-filling-factor asymmetric binary gratings on the top of the solar cells and metallic diffraction gratings as a back reflector. The potential of the structures in the solar cells is investigated by means of numerical simulations, i.e., the rigorous coupled wave analysis enhanced by the modal transmission line theory. The impact of the structure parameters of the gratings on reflectivity is investigated. The results show that a close to zero reflection can be achieved by the two-filling-factor asym- metric binary gratings, and the path length of the transmitted light can be increased within the absorber layer by the metallic diffraction gratings. ©

We present what we believe to be a new technique for the measurement of moderate wedge angles of optical wedge plates using a wedge shear plate (WSP). Using the technique, a wedge angle of up to 5 deg can be measured. The WSP, oriented at an angle to the incident collimated beam, produces shear fringes. The shear fringes are parallel-shifted by rotating a test wedge plate (TWP), in its plane, placed at the input beam of the WSP. The fringe shift is due to the variation of the optical path difference between the interfering beams reflected from the front and back surfaces of the WSP, brought about by the change in the angle of incidence on the WSP due to the rotation of the TWP. The maximum number of fringes shifted as the wedge direction of the TWP (initially aligned perpendicular to the wedge direction of the WSP) is rotated by 180 deg is used for the measurement of the wedge angle of the TWP. Results obtained for a 59.0-arcmin wedge plate with a measurement uncertainty of ±4.68 arcsec are presented. The technique is very simple, and the results are not affected by external vibrations.

The presence of a beam combination system that forms a united image in a common focal plane is one of the features of systems with an optical sparse array. Any control system of a beam combiner has a limited accuracy and, as a result, introduces some optical errors that influence the quality of the united image. This especially concerns systems with a dynamic aperture reconfiguration during an active process of observation. We present analytical expressions for the instantaneous spectral optical transfer function (OTF) of the optical sparse array consisting of N circular and annular subapertures depending on the residual random image alignment and optical path difference errors, and the average OTF for the Gaussian probability distributions depending on the statistical parameters of the last. The formulas are deduced on the basis of the Fraunhofer approach to the Kirchhoff diffraction theory. The results can be used for both space and earth sciences applications.

Methods are described for attenuating solid glass and hollow retroreflectors, without introducing optical path length modifications, for electronic distance measurement. Construction of a prototype novel-design hollow retroreflector is described.

An array of phase retarders can be used as an optical phased array OPA to steer light McManamon et al., Proc. IEEE 842, 268- 298 1996. The introduction of resets enables steering to larger angles without requiring an optical path difference OPD greater than one wavelength. These resets, however, are correct only at the design wave- length. The beam steerer is therefore very dispersive. It has been shown theoretically that resets of an integer multiple of the wavelength will make the beam steerer less dispersive McManamon and Watson, Proc. SPIE 4369, 140-148 2001. We offer the first experimental proof that resets of n are less dispersive than resets of a single . We also show experimentally that the dispersion associated with fixed period resets does vary, but only within a fixed limit. Last, we show the equivalent of power shifting from one order to the next as larger resets move from being divisible by one integer times the nondesign wavelength toward being divisible by the next integer times the nondesign wavelength. © 2005 Society of Photo-Optical Instrumentation Engineers. DOI: 10.1117/1.2149374 Subject terms: spatial light modulators; optical phased arrays; nonmechanical beam steering; broadband beam steering.

The phase shift schlieren (PSS), an improved method of the conventional schlieren imaging technique, enables direct quantitative measurements of optical path length gradients. Like all phase-shifting imaging methods, a successive acquisition of multiple images is required, therefore limiting the PSS use to quasi-steady-state phenomena. We show that PSS can be easily modified to access real-time data. A possible implementation is disclosed, as well as experimental results that validate the method. An application on gas jet is illustrated. We present the features and limitations of the real-time phase shift schlieren (RTPSS).

We describe an optical displacement sensor based on optical feedback interferometry in a blue-light emitting GaN laser diode. Also presented are preliminary results from measuring variations in the optical path length (OPL) of an external cavity (EC) in the 0- to 240-nm range. These results show that, within the specified range, the sensor follows linearly the OPL variation of the EC. Moreover, the slope between a reference and the measured OPL is 1.0003, and the average deviation from the linear slope is 5 nm in this range. Finally, we also consider the stability of the interference signal in long-term measurements.

Proposed and demonstrated is an angstrom level optical path length (OPL) detection sensitivity polarization multiplexed heterodyne acousto-optic interferometric sensor. Because both the phase-coded and the reference rf signals in the design are generated by the same optics, the heterodyne detected rf signals generated contain correlated phase noise characteristics that essentially cancel out during the mixing process in the rf domain. Hence, the proposed four-beam design leads to a super stability OPL sensor with angstrom level experimentally demonstrated measurement stability. A proof-of-concept experiment measures the voltage-dependent phase change due to the refractive index change of a liquid crystal sensor chip.

A linear CCD image sensor is used to electrically scan a measuring point and measure 1-D step-profiles in real time with a sinusoidal wavelength-scanning (SWS) interferometer using double feedback control. In this interferometer, the optical path difference (OPD) and the amplitude of the SWS are controlled so that a ruler marking every wavelength and a ruler with scales smaller than a wavelength are generated. These two rulers enable us to measure an OPD longer than a wavelength in real time. Two different step profiles with step heights of 1 and 20 μm, respectively, are measured with a measurement error of less than 8 nm. Measuring time for one measuring point is 0.04 s.

A laser with its wavelength stabilized to a Fabry-Perot etalon has many industrial applications. An ideal error signal for laser stabiliza- tion is the dispersion-like signal generated without wavelength modula- tion. We present a technique, by which the error signal is generated by the difference of two resonance peaks of a Fabry-Perot etalon. A laser beam is split into two beams, which pass through an etalon with a small optical path length difference to generate two partially overlapped reso- nance peaks. Subtracting one peak from the other yields a dispersion- like error signal. The zero crossing of the differential signal is insensitive to the angle drift of the etalon if the incident angles of the two laser beams are nearly equal but with opposite sign. © 2004 Society of Photo

A high-accuracy absolute measurement system of the refractive index of air is proposed. The measurement of the instantaneous index of refraction is achieved by comparing two laser optical paths with a differential laser interferometer. The vacuum optical path length is varied via a motor-driven trapezoidal vacuum cavity moving through a known distance. Compared to other measurement methods, the sealed vacuum cavity requires no vacuum pumping between measurements, and allows this method to function well in industrial applications. The measurement accuracy is better than 5×10–8.

A laser beam is used to determine the radius of curvature of a material surface. For this, an equation relating the radius of curvature of a material surface to the curvature of a laser wavefront and the spot radius of a laser beam, and the optical path length, is first established. Then, by substituting the calculated radius of the wavefront curvature at the sample, the measured spot radius of the beam at the sample, and at the testing plane in the equation, the radius of curvature of the sample surface can be determined. Furthermore, the optical-lever method to determine the surface's curvature has practical application. A comparison between results obtained with the proposed and optical-lever methods is made. The two sets of values yield the radii of surface curvature that are in good agreement. But if the experimental layout, signal detection, and measuring capability are also compared, the proposed method is superior to the optical-lever method.

Phase difference amplification is a technique used to produce a fringe contour map in which the optical path difference between one fringe and the next is a fraction of a wavelength. To ensure high accuracy of the technique, it is usually necessary to generate interference between the high-order diffracted beam and its conjugate beam by means of a holographic recording material that provides sufficiently large nonlinearity to record the original fringe pattern from the test object. This paper shows that not only the nonlinearity of the recording material, but also multiple-beam interference, can be used to produce high-order diffracted beams. A Tolansky-type multiple-beam interferometer has been used in conjunction with an optically addressed liquid-crystal spatial light modulator to set up a system that functions in near real time and provides high accuracy.

We propose a coherent lightwave neural network system whose behavior can be controlled by the lightwave carrier frequency. We utilize the dependence of homodyne interference on the lightwave frequency by choosing the optical path lengths of the signal and the reference to be slightly different. The synaptic weights consist both of the optical path difference and variable delay realized by a spatial light modulator. A frequency-dependent learning is performed by a novel complex-valued Hebbian rule associated with the carrier frequency. Experiments demonstrate that the associative memory recalls different complex-amplitude patterns according to the carrier frequency variation successfully.

To produce stable beams used by pencil beam interferometers, a new equal optical path beamsplitter (EBS) is developed. The beamsplitter divides one incident pencil beam into two parallel exiting beams with a fixed separation. The new EBS is a monolithic unit comprised of two right-angle trapezoidal prisms with a thin film beamsplitting coating on the faces, which are cemented together. Adjusting the dimensions of each element according to a simple algebraic relation produces two identical, parallel beams separated by a fixed distance with a zero optical path difference between them. The monolithic EBS is very simple and stable. It has applications in interferometers that require the use of a pencil beam source, such as the long trace profiler (LTP) and the precise angle monitor. If a large-diameter wavefront is incident on the EBS, it can be used in shearing interferometer applications, such as the lateral translation shearing interferometer and the rotational shearing interferometer. Use of the EBS in all of these configurations significantly improves instrument stability and accuracy. Some application examples and test results are presented.

The dynamic response of a fiber optic Bragg grating to mechanical vibrations is examined both theoretically and experimentally. The theoretical expressions describing the consequences of changes in the grating's reflection spectrum are derived for partially coherent beams in an interferometer. The analysis is given in terms of the dominant wavelength, optical bandwidth, and optical path difference of the interfering signals. Changes in the reflection spectrum caused by a periodic stretching and compression of the grating are experimentally measured using an unbalanced Michelson interferometer, a Michelson interferometer with a nonzero optical path difference. The interferometer's sensitivity to changes in the dominant wavelength of the interfering beams is measured as a function of interferometer unbalance and is compared to theoretical predictions. The theoretical analysis enables the user to determine the optimum performance for an unbalanced interferometer.

White-light interferometry (WLI) for object topography measurements relies on an accurate rate of change of the optical path difference (OPD) between the object and reference beams. However, the motion of the scanner realizing the OPD change is not perfect, and scanning errors directly impact measurement accuracy. We describe a white-light interferometer that is capable of accounting for these errors and correcting them in real time through the monitoring of the scanner motion. This monitoring is achieved by embedding an additional high-coherence interferometer into the system. Besides allowing for monitoring the scanning progress, this system also provides the means to automatically calibrate the WLI. Significant improvements both in the accuracy and repeatability are demonstrated experimentally. Data analysis is discussed as well.

Design considerations for a Nomarski reflection microscope to produce a desired differential interference contrast image and the re- sults are presented. Formulas for tracing of rays through the Nomarski prism and calculation of the optical path difference and the angular sepa- ration between the orthogonal linearly polarized components and for de- termining the position of the ray intersection plane are devised. Tech- niques for the design and fabrication of a Nomarski prism and a complete differential interference contrast microscope are described. © 2003 Society of Photo-Optical Instrumentation Engineers. (DOI: 10.1117/1.1590320) Subject terms: differential interference contrast microscope; Wollaston prism; Nomarski prism; surface microroughness; optical path difference; extraordinary and ordinary rays.

A novel method for nanometer indicating based on surface plasmon resonance (SPR) is introduced. A fiber probe with a semispherical end approaching a coated Kretschmann (1971) prism is equivalent to a four-layer prism-metal-air-fiber structure. Theoretical analysis shows that the transmitted intensity coupling into the fiber probe changes as the thickness of the air gap varies. Owing to this property, a noncontact nanometer indicating system can be built. The SpR nanometer indicator can be integrated into a heterodyne interferometer to reduce drift. Askew retroreflector is designed so that the incident angle of its first reflection surface is equal to the resonance angle of SPR to implement the integration SPR indicating experiments show that a maximum deviation of 12 nm and a resolution of 0.1 nm/nV can be achieved. Moreover, the uncertainty of an integrated interferometer whose optical path difference is 300 mm is reduced from 60 to 10 nm when air-conditioning is 0.5 °C/h.

A novel technique for the transmission of optical length information using a low-coherence tandem interferometer and a single-mode optical fiber is developed. The optical path length with a step gauge in the first low- coherence interferometer is transmitted through the optical fiber to the second interferometer. The interference fringes containing the length information of the gauge are generated with high accuracy by compensating the optical path difference in the second interferometer.

An all optical ultraminiaturized sensor head for displacement measurement that has a size of less than 5 mm in square has been produced. The sensor works by means of optical triangulation. To achieve the optical function, the sensor consists of a three-layer polymer waveguide patterned by deep x-ray lithography (LIGA), a light input fiber, two detection fibers, and microcylindrical lenses, which are also fabricated by deep x-ray lithography. The fibers and the cylindrical lenses are placed into the waveguide without any active alignment by using the waveguide walls as guiding and fixing structures. The ratio of the intensities detected in the two detection fibers is the measure of the distance between the object and the sensor. High resolution of about 10 ?m is achieved in the range of 2 to 3 mm between the sensor and an object with a diffusively reflecting surface.

Thermal effects are investigated using laser interferometric and infrared thermometric techniques in diode-end-pumped solid state lasers operating under lasing and nonlasing states. The laser interferom- etry provides high resolution to determine the optical path difference (OPD) induced by thermal effects of the crystal. The infrared thermom- eter measuring the temperature distribution at the end pump face is pro- posed to evaluate the thermal lensing power induced by the index part. It is found that the temperature variations across the crystal face under nonlasing operation increase 20 to 27% compared with lasing conditions in Nd:YVO4 crystals. Thermal lensing power under the actual lasing con- dition is measured to be 0.2 m 21 to 2.1 m 21 with the pump power ranging from 1 to 8.3 W; the index part takes the proportion of about 59% in the total thermal lensing effect for end-pumped Nd:YVO4 lasers. © 2001 So

Measurement of differences in optical path length in monochromatic light with any interferometric method is insensitive to errors that are whole numbers of waves. If measurements are performed in s ...