Table of contents

The articles in this special feature of Measurement Science and Technology are devoted to an exciting area of fluid metrology pursuing the registration of flow velocities in three dimensions by particle holography—commonly termed holographic particle image velocimetry (HPIV) (Hinsch 2002). Already in 1993 this technique was considered to 'revolutionize the acquisition of velocity data in much the same way as did the inventions of hot wire anemometry and laser Doppler velocimetry' as E P Rood states in his foreword to the proceedings of the first workshop dedicated to the topic at the Washington ASME Fluid Engineering Conference (Rood 1993). The big step forward is to eliminate most of the depth-of-focus restrictions of classical PIV by a holographic recording of tracer particles. Thus, even non-stationary flows can be registered in a single record.

A central concern of the early days was to explore optical set-ups suitable for improving particle-position resolution by using large recording apertures and for suppressing coherent noise. Furthermore, the evaluation of the holographic images required efficient hardware and software to scan and process the coordinates of particle images in a reasonable time. A sophisticated system relying on the state-of-the art experience and the utmost in processing hardware was producing first fields of thousands of three-dimensional velocity vectors (Barnhart et al 1994). Much profound research work on the main issues has been carried out in the meantime. Advances toward practical systems, however, needed fuelling by the recent technological developments of high-energy pulsed lasers and electronic image acquisition as well as the increasing performance of digital image processing.

This recent progress led to a session on HPIV during the international PIV'01 conference at Göttingen, Germany (Kompenhans 2001), the creation of a worldwide working group (photon.physik.uni-oldenburg.de/hpiv) and in May 2003 an international workshop on holographic metrology in fluid mechanics at Loughborough University, UK (Coupland 2003). These workshop presentations have been elaborated and supplemented in the present special feature.

The holographic velocimetry work presented here can be grouped into two sections according to the type of hologram recording—using either a physical carrier material or an electronic image sensor. Most researchers still use the somewhat anachronistic silver-halide emulsion of photographic film, especially when high resolving power is needed as in several application-specific topics. It offers still an unequalled resolution of up to 5000 line-pairs/mm at reasonable sensitivities to record even the low-power light scattered by tiny tracer particles, yet it requires laborious wet chemical processing.

A good impression of the huge amount of data that can be stored on photographic film and the immense effort needed to analyse the reconstructed holographic images is given in the paper by E Malkiel et al. A straightforward in-line recording layout was chosen for the submersible recording system employed in marine studies. An efficient analysis of hundreds of holograms is achieved with an automated scanning system incorporating an optical band-pass filter to suppress speckle noise and to detect small tracer particles even in the neighbourhood of much larger `particles' like copepods that are screened by a segmentation routine. Data flow is economized by a new and highly efficient compression method.

While the disturbing effect of speckle noise is much relaxed in the widely used off-axis recording it still has a considerable impact when large and densely seeded volumes are under investigation. Light-in-flight holography (LiFH)—a way to suppress noise by coherence reduction—is applied to a large wind-tunnel flow in the paper by S F Herrmann and K D Hinsch. While a complete deep-volume field is recorded, the effective depth during the read-out process can be reduced to avoid noise from too many out-of-focus particle images. Analysis of the digitized real-image particle field is done by direct 3D correlation of grey-values from depth-scans. Based on the same experimental data a paper by K Hinsch and S F Herrmann explores in detail the gain in signal-to-noise ratio (SNR) for digitized image planes and describes the performance of LiFH versus normal holography based on speckle theory.

Reconstruction from a double-exposure hologram permits direct correlation of the complex amplitude of the particle fields locally in a method called object conjugate reconstruction (OCR), which is presented in a new configuration (transmission) in the paper by R Alcock et al. The technique is ideally suited to measuring within thick glass cylinders (engine research) because it dispenses with the need to correct for distortions by use of holographic optical elements. Instead, a ray tracing analysis is used for correct mapping.

Holographers have tested many alternative materials to avoid the time delay and effort in processing standard photographic film, all of which still show at least a major disadvantage in resolution, sensitivity or handling. More recently a genetically modified version of the photochromic protein bacteriorhodopsin (BR) has been introduced to HPIV measurements. It offers perfect resolution and sufficient optical sensitivity and is examined extensively here. D Barnhart et al explain BR's basic properties and propose a variety of new configurations, also utilizing its ability to alter the state of polarization in the reconstruction. Though the storage time of BR holograms is limited to a few minutes when the same wavelength is used for readout, V S S Chan et al have realized a first application of double-exposure HPIV. They also introduce further concepts to achieve multiple holograms in BR. In conclusion, BR is considered the most promising candidate to replace silver-halide photographic film, and also for intermediate storage of holograms to be scanned and processed digitally.

Two of our papers consider holographic tools for tasks in fluid dynamics other than velocimetry. I Shimizu et al are concerned with the discrimination of size and shape from arbitrarily positioned particles by reviving a historical concept of multiplexed matched spatial filtering in which a special type of hologram is used for pattern recognition purposes. Automated in-place processing is achieved with photoconductor plastic holograms (PPH). Holographic interferometry is used by S-J Lee and S Kim in the study of quasi-two-dimensional Hele–Schaw convection to visualize temperature distributions. The results are compared with those obtained from velocity mapping by conventional PIV.

The second half of our contributions are dedicated to the challenge of performing particle holography digitally. This reflects the need to overcome the essential bottlenecks of classical particle holography: the time delay and cumbersome processing by photographic recording, the difficulty of recording time series and the experimental effort needed to extract particle coordinates in three dimensions—these are severe obstacles on the way towards a tool of general practical applicability. For an estimate of its potential, recall the breakthrough of 2D PIV when it turned from photographic to CCD recording!

A digital hologram that consists of an array of intensity values stored in a computer memory, of course, does not provide the beauty of viewing a live reconstructed three-dimensional image. However, this is not the aim of particle holography, since the end data—coordinate values and displacements for a large number of particles—must be extracted laboriously from the reconstructed real images of the particle field anyway. We don't need the physical wave reconstruction and might just as well represent it by appropriate computer routines. Yet, the performance of typical CCD sensors still falls short of that of photographic film. Any holographic set-up must take into account that, due to the size and number of pixels, resolution in the hologram is less by a factor of about 10 and the number of resolvable elements less by a factor of 10000. This imposes restrictions on interference angles and field width—a challenge to the creativity of researchers, who each propose specific solutions.

Two papers address the problem of inferior longitudinal resolution in completely digital HPIV caused by the small CCD aperture. H Meng et al obtain a greatly improved depth discrimination by the utilization of phase information in the particle image field—data that are specific for digital reconstruction and not available in the commonly used intensity fields. The vector plot of results from a water jet flow illustrates the state-of-the-art of the technique and can stand comparison with traditional results. This paper may also be considered a good introduction to the topic, a comprehensive overview of HPIV systems operated worldwide and a summary of the critical issues in digital particle holography. C Fournier et al observe axial oscillations of particle image intensity that impede focus finding and are remedied by proper aperture windowing.

The CCD problem is avoided when traditional recording is accepted and only the reconstruction is done digitally—as shown in the paper by H Yang et al. The lengthy scanning and correlation of 3D image fields is now replaced by 2D high-resolution digitization of intermediate holograms on 35 mm film and complex correlation operating with these data. In the presentation by M Malek et al three-dimensionality is confined to space while velocity is restricted to two components. Particle displacements within a set of transverse planes are then obtained by conventional particle tracking algorithms. J Müller et al show in their application-oriented study of the atomization of molten metal that a CCD-based in-line hologram with resolution improved by relay imaging provides satisfactory data for the numerical reconstruction of particle location and size.

J Coupland presents some thought-provoking ideas to tackle under-sampling by the widely spaced CCD pixels. When the optical field of a particle image is known, model fitting can compensate for the loss of information. Additionally, annoying replicas of particle images may be avoided by a non-periodic array of sampling apertures. Finally, J Lobera et al explore a different version of holography for PIV applications, i.e. digital speckle pattern interferometry (DSPI), a technique well established for deformation contouring in optical metrology. Here, image plane holograms of single planes in the fluid flow map particle displacements with interferometric sensitivity—a means to greatly improve depth resolution.

We are convinced that our collection of papers is a comprehensive presentation of the state-of-the-art in this innovative field of fluid metrology. It serves to further exchange between the research groups involved and should inform and stimulate those looking for non-conventional solutions to their metrological challenges.

The editors appreciate very much the stimulating cooperation with the staff of Measurement Science and Technology, especially with S D'Souza-Harris, the cooperative assistance of our writing colleagues, and the kick-off role played by N Halliwell and J Coupland of Loughborough Technical University, who organized a challenging meeting that served to share scientific experience and consolidate personal friendships.

References

Barnhart D H, Adrian R J and Papen G C 1994 Phase conjugate holographic system for high resolution particle image velocimetry Appl. Opt.33 7159–70

Coupland J (ed) 2003 Workshop on Holographic Metrology in Fluid Dynamics, Loughborough CD-ROM Proceedings

Hinsch K D 2002 Holographic particle image velocimetry Meas. Sci. Technol.13 R61–72 (IOP Article)

Kompenhans J (ed) 2001 4th Int. Symp. on Particle Image Velocimetry, Göttingen CD-ROM Proceedings

Rood E P (ed) 1993 Holographic Particle Image Velocimetry (ASME FED 148) (New York: ASME)

Scanning and analysis of reconstructed holograms of a one-litre sample volume containing particles with varying sizes and shapes at high resolution is a major challenge. A completely automated system for analysing in-line holograms recorded in the ocean, which resolves particles larger than 10 µm, has been developed. It measures the three-dimensional coordinates of all the particles within the reconstructed volume and records their in-focus images. Scanning and analysing a reconstructed volume of about 500 cm³ that contains several thousand particles takes about 5 h. The analysis consists of several steps. After compensating for exposure non-uniformities, the reconstructed images are scanned continuously with a digital camera. Then, superposition of thresholded images weighted by depth is introduced as a method compressing the 3D data to a plane to increase the efficiency of segmentation analysis. Subsequently, edge filtering is used for pinpointing the depth coordinate. To detect particles smaller than 50 µm, the reconstructed images are band-pass filtered optically. This approach is based on analysis that identifies interference of the reference beam with off-axis scattered light as the primary contributor to background noise. The scanning, thresholding and edge detection processes are repeated for the small particles. Additional procedures remove duplicate detections, and post-processing classifies the particles based on geometrical parameters. Sample data are presented.

Holographic particle imaging techniques for air-flow investigations are mainly limited to small-scale laboratory experiments. The two main reasons are the limited light power available in conjunction with small tracer-particle sizes, which must be in the order of 1 µm to properly probe air flows, and the increased background noise from out-of-focus particles in deep volumes preventing investigations with higher particle densities. To ensure a good accuracy of the velocity measurements by faithful reconstruction geometry, the evaluation of particle images is often conducted in the original recording set-up. The time-consuming scanning process, however, blocks the flow facility during evaluation—a disadvantage for measurements in costly industrial wind tunnels. For an alternative, we have introduced off-site reconstruction and evaluation. In recent papers we have furthermore demonstrated principles to cope with little object light and to suppress background noise. Here we present a successful implementation of theses principles for wind-tunnel measurements.

Particle holography has proven to be a useful metrological tool for three-dimensional flow velocimetry. To cope with the problem of noise from out-of-focus particles the technique of light-in-flight holography (LiFH) has been introduced that utilizes properties of a laser source of short coherence. While the feasibility of the method has been shown earlier, a more profound quantitative analysis of its performance was still required. The present paper briefly summarizes some essential knowledge on noise in particle holograms, reviews recent approaches for handling noise in deep-field particle holography and presents first experimental checks of these concepts on short-exposure holographic recordings of particle fields in a wind-tunnel flow. The performance of ordinary and short-coherence particle holography are compared directly by operating the same laser in either long-coherence or short-coherence mode. It is established experimentally that performance is also related to laser beam quality.

This paper reports on a new holographic particle image velocimetry configuration and analysis procedure that can be used to measure particle displacement through thick distorting windows. The technique builds upon the scanning fibre probe based object conjugate reconstruction geometry; however it avoids the requirement of using a holographic optical element to correct for window distortion of the beams. Removal of the distortion is instead accomplished by using a ray trace mapping between the wave vectors scattered by the particles at the time of each exposure and those measured by the interrogation system. The technique is ideally suited to the study of flow structure within the combustion chamber of a diesel engine, and preliminary experimental results that attempt to assess the accuracy of the technique in this situation are presented.

Recent trends in optical metrology suggest that, in order for holographic measurement to become a widespread tool, it must be based on methods that do not require physical development of the hologram. While digital holography has been successfully demonstrated in recent years, unfortunately the limited information capacity of present electronic sensors, such as CCD arrays, is still many orders of magnitude away from directly competing with the high-resolution silver halide plates used in traditional holography. As a result, present digital holographic methods with current electronic sensors cannot record object sizes larger than several hundred microns at high resolution. In this paper, the authors report on the use of bacteriorhodopsin (BR) for digital holography to overcome these limitations. In particular, BR is a real-time recording medium with an information capacity (5000 line-pairs/mm) that even exceeds high resolution photographic film. As such, a centimetre-square area of BR film has the same information capacity of several hundred state-of-the-art CCD cameras. For digital holography, BR temporarily holds the hologram record so that its information content can be digitized for numeric reconstruction. In addition, this paper examines the use of BR for optical reconstruction without chemical development. When correctly managed, it is found that BR is highly effective, in terms of both quality and process time, for three-dimensional holographic measurements. Consequently, several key holographic applications, based on BR, are proposed in this paper.

This paper demonstrates the use of bacteriorhodopsin (bR) as the holographic recording medium for a holographic particle image velocimetry (HPIV) system. Using an off-axis hologram in bR, double-exposed images of particles in a turbulent flow are recorded. A high numerical aperture configuration (NA = 0.75) ensures a maximal signal intensity of the holographic recordings. Using a CCD the real particle images, that were reconstructed in the original object space, were digitized. The reconstructed image has a theoretical depth of focus of 4.73 µm and a diffraction-limited resolution of 0.43 µm. Using a priori knowledge about the flow, the flow pattern is extracted from the double-exposed particle images. A liquid crystal shutter was employed during the reconstruction in order to minimize photo-induced erasure. Details of the experimental set-up, as well as the difficulties which were encountered during this investigation, are discussed in this paper. The paper also discusses various multiplexing methods and their suitability for use with bR to remove directional ambiguity in HPIV.

A new technique for rapidly discriminating shapes and/or sizes of micrometre size particles which are spatially distributed on a large scale has been developed. The technique is based on multiplexed matched spatial filtering, which is a kind of Fourier holographic filtering technique. Using the technique, large view visualization of the spatial distribution and the spatial behaviour of specific particles (e.g. aerosols, allergen particles, red blood cells, etc) can be realized. To make the multiplexed matched spatial filter (MMSF), a new material for hologram recording has been applied. The material is a photoconductor plastic which is processed by a solvent vapour and a corona discharge. The method of hologram recording is a dry process, which processes the material in several minutes at the initial settings of the device. Therefore, the MMSF can be made very easily in a short time. In the research, the discrimination of spatial behaviour of moving particles of different shape and/or size has been carried out by the MMSF made by the photoconductor plastic material.

Variations of temperature and velocity fields in a Hele–Shaw convection cell (HSC) were investigated using a holographic interferometry and 2D PIV system with varying Rayleigh number. To measure quasi-steady variation of the temperature field, two different measurement methods of holographic interferometry—the double-exposure method and the real-time method—were employed. In the double-exposure method, unwanted waves were eliminated effectively using a digital image processing technique. The reconstructed images are clear, but transient flow cannot be reconstructed clearly. On the other hand, transient convective flow can be reconstructed well using the real-time method. However, the fringe patterns reconstructed by the real-time method contain more noise than the double-exposure method. Experimental results show a steady flow pattern at low Rayleigh numbers and a time-dependent periodic flow structure at high Rayleigh numbers. The periodic flow pattern at high Rayleigh numbers obtained by the real-time holographic interferometer method is in good agreement with the PIV results.

Holographic particle image velocimetry (HPIV) offers potentially the best solution to volumetric measurements of the three-dimensional velocity fields in complex flows. However, the traditional film-based HPIV measurement is rather cumbersome, limiting its use to only a handful of groups worldwide. The newly emerged digital HPIV revolutionizes flow measurement science by providing a practical 3D velocimetry tool. It commands simple hardware that is similar to regular two-dimensional particle image velocimetry (PIV), yet it provides continuous (time-series) three-dimensional, three-component flow field data. Not only is the need for chemical processing eliminated, but also the cumbersome optical reconstruction is completely replaced by numerical reconstruction algorithms. Several breakthroughs have led to the development of the first practical and integrated digital HPIV systems. To explain the transition from film to digital recording, fundamental issues in HPIV are reviewed in this paper. Axial accuracy in HPIV measurement is ultimately limited by an inherent depth-of-focus problem, while information capacity is limited by inherent speckle noise. Information capacity is an important concept in HPIV, comprising the maximum acceptable seeding density multiplied by the sample volume depth along the optic axis. Both the axial accuracy and the information capacity are limited by the effective hologram aperture. The pursuit of a large hologram aperture in the past has resulted in further complexity in film-based HPIV systems. Digital HPIV, on the other hand, enjoys great simplicity of implementation and operation. A digital HPIV is also far more compact and rugged compared to existing film-based HPIV systems, making it suitable for duplication and commercialization. However, since digital sensors suffer from inferior pixel resolutions compared to films, the effective hologram aperture is much smaller in digital HPIV than that achievable in film-based HPIV. Alleviating this problem, digital HPIV also presents new possibilities in data processing such as the use of the complex amplitude of the reconstructed light wave to improve depth sensitivity and signal-to-noise ratio. Two examples of digital HPIV systems and measurement results are given. We believe digital HPIV can revitalize holographic particle imaging and bring it into the mainstream in much the same way that digital PIV brought PIV into widespread use a decade ago.

The numerical reconstruction of an in-line digital hologram is a critical point in digital holographic particle image velocimetry. In particular, the shape of the axial profile of the reconstructed particles plays an important role in depth recovery. We show that this profile presents some oscillations when reconstructing by convolution with the Fresnel function. A window can be introduced in the expression of the reconstruction function in order to control these oscillations. The effects of this windowing are discussed and a criterion for the choice of window is given. The method is then illustrated by the processing of a digital hologram of Lycopode particles.

We have recently proposed a new method to extract the three-dimensional (3D) velocity vector data from double-exposure holographic particle image velocimetry (HPIV), which we call the digital shearing method. In contrast to the full 3D correlation, it has been shown that all three components (3Cs) of particle image displacement can be retrieved using six two-dimensional fast Fourier transform operations and appropriate coordinate transformations. In this paper we demonstrate the capabilities of this approach on actual HPIV data.

The holographic recording method described uses an imaging system to record a hologram of high numerical aperture using a conventional 35 mm film. The holograms are digitized and particle images are reconstructed numerically. From particle images reconstructed from separate holograms, we illustrate the analysis process by computing the 3Cs of particle image displacement in a step-by-step manner.

We have used a digital in-line holography system with numerical reconstruction to determine 2D velocity fields in several slices of a sample volume. This system records directly on a charge-coupled device (CCD) camera the diffraction patterns of small particles illuminated by a double-pulse laser diode. The numerical reconstruction is based on the wavelet transformation method. A slice is reconstructed by computing the wavelet components for different scale parameters. These parameters are related to the axial distance between a particle and the CCD camera. The particle images are identified and localized by analysing the maximum of the wavelet transform modulus and the width of the particle image (L₅₀). Afterwards, a point-matching algorithm is applied to the set pairs containing the particles. This step is followed by velocity vector extraction. The details of the velocity extraction and the data processing method are presented and the simulations and experimental results are discussed.

An application of digital inline holography to a metal spray-forming process is presented. In contrast to conventional 2D techniques such as particle image velocimetry (PIV) it is possible to capture the 3D particle distribution at once. From the reconstructed hologram the size of the particles can also be extracted. A plane wave passes the particle stream and the diffracted wave is recorded by a CCD sensor using a lens to image the sample volume closer to the sensor. The reconstruction of the particle distribution is performed numerically in the computer and provides direct access to the intensity and the phase of the recorded wavefront. A brief introduction to digital holography will be given and the process of spray forming will be described. An intensity-based algorithm is applied to detect the particles. Recent measurements of the spray-forming process are presented and the suitability of this technique for industrial applications is demonstrated.

Holographic particle image velocimetry (HPIV) has now been demonstrated by several research groups as a method to make three-component velocity measurements from a three-dimensional fluid flow field. More recently digital HPIV has become a hot topic with the promise of near-real-time measurements without the often cumbersome optics and wet processing associated with traditional holographic methods. It is clear, however, that CCD cameras have a limited number of pixels and are not capable of resolving more than a small fraction of the interference pattern that is recorded by a typical particulate hologram. In this paper, we consider under-sampling of the interference pattern to reduce the information content and to allow recordings to be made on a CCD sensor. We describe the basic concept of model fitting to under-sampled data and demonstrate signal recovery through computer simulation. A three-dimensional analysis shows that in general, periodic sampling strategies can result in multiple particle images in the reconstruction. It is shown, however, that the significance of these peaks is reduced in the case of high numerical aperture (NA) reconstruction and can be virtually eliminated by dithering the position of sampling apertures.

In this paper digital speckle pattern interferometry (DSPI) as a digital image plane holography (DIPH) technique is presented and its potential for fluid velocimetry are discussed. The recording is carried out with a spatial phase shifting (SPS) DSPI set-up, which can also be viewed as an off-axis DIPH set-up. A theoretical study of both SPS–DSPI analysis using a Fourier transform method and DIPH analysis is presented for a set-up with only one illuminated plane. From the DIPH analysis, a way to extend the SPS–DSPI set-up to simultaneously record but independently reconstruct several fluid planes is inferred. Some preliminary results from a convective flow illustrate the feasibility of the quasi 3D recording.

In this paper, we introduce a non-invasive high-resolution imaging technique, called Doppler optical coherence tomography (DOCT), to visualize the structural and fluid flow information in the complex flow geometry for industrial applications. The technique is based on the combination of laser Doppler velocimetry with the recently developed optical coherence tomography to obtain simultaneously high-resolution tomographic images of static and moving constituents in highly scattering media. It is shown that DOCT is capable of non-invasively monitoring complex flow geometry with a volumetric resolution of about 10³ cubic micrometres.

The present study considers an autofocusing laser probe system used for the measurement of the surface profile and roughness of an object. The system is based upon a modified pickup head of a commercially available DVD player which uses a voice coil motor (VCM) to drive an objective lens during the autofocusing process. It is known that hysteresis of the VCM during the autofocusing process reduces the precision of the measurement results. Consequently, the present investigation adopts a hysteresis model to develop a compensation method which can improve the accuracy of the optical pickup head within the measurement system.

A multi-wavelength diode laser interferometer for measurement of surface profiles has been developed. Three laser diodes emitting in the near infrared were used. The resulting synthetic wavelengths were approximately 14 µm and 290 µm. The long synthetic wave leads to a measuring range of ≈145 µm without counting the interference fringes. The result is used to determine the fringe order of the 14 µm synthetic wave and finally the fringe order of the optical waves within the measuring range. By modulation of the diode currents with different frequencies around 1 MHz, wavelengths are also modulated. The interferometer output contains harmonics of the modulation frequencies. Using a lock-in technique the interferometer signals from the three laser diodes are detected simultaneously with only one photodetector. For measurements of surface profiles the beams are focused on the sample. The surface is scanned by moving the sample in the x- and y-directions with mechanical translation stages.

A new method is proposed for measuring the loss tangent of flat substrate materials using the split cylindrical resonator method. It is based on a full-wave analysis and a rigorous mode match solution for the TE₀₁₁ mode. The dielectric losses of several commercial substrates have been measured. The results demonstrate that the proposed non-destructive method is capable of accurately characterizing the dielectric loss of flat substrate materials.

The computational methods for complex dielectric permittivity data treatment are considered in this paper. The dielectric spectroscopy data analysis in the frequency domain can be reduced to the problem of choosing the appropriate model functions and an estimation of their model parameters. To address the latter problem a method has been formulated based on a penalized maximum likelihood approach, for obtaining a smooth estimate for the model parameters expressed as functions of temperature. The use of the Hilbert transform (Kramers–Kronig relation) for dc conductivity evaluation directly from the complex dielectric permittivity data has been explored as well. In this paper a numerical algorithm for this procedure, using the fast Fourier transforms and a suitable interpolation technique, is suggested. Based on these methods, state-of-the-art software for dielectric spectroscopy data analysis in the frequency domain has been developed.

In the process of initial alignment for a strapdown inertial navigation system (SINS) on a stationary base, the east gyro drift rate is an important factor affecting the alignment accuracy of the azimuth misalignment angle. When the Kalman filtering algorithm is adopted in initial alignment, as the east gyro drift rate cannot be estimated, it yields a constant error in the estimation of the azimuth misalignment angle. In this paper, a novel method is proposed to improve the alignment accuracy. The update equation for the estimate of the east gyro drift rate is established, and the estimation accuracy of the azimuth misalignment angle has been improved greatly through adjusting the estimated value of the east gyro drift rate on the basis of the update equation. Simulation results show that the method proposed in this paper is efficient in initial alignment for a medium accuracy SINS on a stationary base.