Laser speckle

Origin of speckle

A phenomenon of light illumination unnoticed by most people is its granular structure, which is normally smoothed by the mixing of different colors in lampor natural sources of light, but which can also be observed in certain circumstances, such as during the twinkling of stars or the dancing colors of the sun’s rays transmitted through the leaf cover of trees. Many scientists have investigated this granularity since the time of Newton (1642-1727), who noticed that the scintillation or twinkling could be observed for stars, but not for the planets.1 Today, speckle is casually seen as the intensity and color fluctuation in the distant headlights of a car, or as a mottled light pattern on rear projection screens. Speckles can even be seen in the security holograms on credit cards, which can easily be studied with a magnifying glass.

Since the invention of the laser in 1960, there has been a growing interest in the speckle phenomenon, since color smoothing is not present in monochromatic light, and speckle patterns become clearly visible with laser illumination of the surface of many objects. For this phenomenon, it is necessary that the object diffuses the light like a piece of paper, an unpolished metal surface, or that the light propagates through a medium with randomly refractive index fluctuations. On the other hand, no speckle is observed by specular reflection of laser light on polished surfaces such as mirrors, or by laser light transmission through non-turbid liquids or clear glass-like lenses – with the exception of speckles generated at the end of multimode fibers.

From this we can conclude that speckle arises from the splitting of the coherent laser beam into a

number of wavelets originating from microscopic elements in the medium, which travel over unequal distances to every point in space surrounding the surface, where they interfere with random but stable phase differences, leading to a time-independent fixed 3-D intensity pattern. If the observation point is moved, the path lengths travelled by the scattered components change, and a new independent value of intensity may result from the interference process. The typical appearance of speckle is depicted in Figure 1 in the case of the scattering of a laser beam from a diffuse surface, which looks similar to a mixture of grains of salt and pepper.

Since a stable interference occurs at every point in space, a photographic plate placed at any distance from the object can record the speckle pattern as shown in Figure 1 (objective speckles). If the photographic plate is replaced by an imaging system such as the human eye, shown in Figure 2, the pupil can be considered a new source of wavelets of a random phase, where they are additionally diffracted and imaged by the eye lens on the retina.

The interference between these diffraction images is responsible for the random 2-D intensity distribution on the retina, sensed as a granular structure (subjective speckle).

A prerequisite for the development of speckle is either sufficient temporal or spatial coherence of the light source. Temporal coherence of a light source is defined as the maximum time delay ∆t between two or more light waves emitted by the source, where the phase shift between the waves in the course of time is stable enough for their interference. This corresponds to a path difference ∆lt of the waves in the direction of the light propagation, given by the relation:

Fig. 1. Speckle pattern generated on a rough surface illuminated by a laser.

∆lt = c ∆t

where c is the speed of light. Only waves with a shorter path difference than ∆lt can contribute to a speckle pattern. This path difference, called coherence length ∆lt, depends on the spectral bandwidth of the light source ∆λ by the relationship:

∆lt = λ2/∆λ

White light at the mean wavelength of λ = 0.5 µm and a bandwidth of ∆λ = 350 nm has a coherence length of less than 1 µm, but a laser with a spectral bandwidth of 0.001 nm has a coherence length of 25 cm.

Since the average roughness of diffuse surfaces is much greater than 1 µm, the number of waves passing a point in the space near to a rough scattering surface, which can interfere, is extremely low by illumination with white light, but is very high for laser light, which explains the pronounced speckle pattern produced by laser light, contrary to that of a white light source.

However, there is also a second condition necessary for the development of speckle. If the size of the illuminated spot on a scattering surface, or the light source itself, is very small, the phase shifts between waves in a direction transversal to the wave propagation direction from the source become stable enough to interfere – thereby generating a speckle where the waves do overlap, for instance, with the help of an imaging lens, and the source is said to be spatially coherent. The largest transversal distance of waves with a stable phase shift, called spatial coherence length ∆lr of the source, is

produced by:

∆lr = λ z/ds = λ/θ

where λ is the mean wavelength, ds the diameter of the source, and z the distance between the source and the observation point, and the ratio:

θ = ds/z

is equal to the apparent angular size of the source at the observation point. This relationship tells us that a small incoherent light source with a broad spectral bandwidth, and thus low temporal coherence, can possibly possess sufficient spatial coherence to produce speckle. As mentioned above, this can happen with several natural and technical light sources with a broad spectrum, such as the sun, the stars, or lamps, if they are far enough from the observer.

To obtain an estimate of this effect, we have to look at the spatial coherence corresponding to the resolution limit of the human eye of 1 arcmin, which is equal to θ = 3 × 10-4 rad at λ = 0.5 µm, with ∆lr = 1.4 mm. As a consequence of this, a star with a much smaller apparent angular size than this resolution limit of the eye has a spatial coherence length much larger than the diameter of the pupil. It then becomes clear that refractive index fluctuations in the atmosphere induced by winds or turbulence can generate slowly varying interference on the retina, seen as scintillation of the starlight. As Newton pointed out, this is much less noticeable for the planets, because of their larger apparent size and, consequently, their lower spatial coherence. A speckle due to the spatial coherence of laser source illuminating the retina of the eye can also be generated due to fluctuation in the refractive index of the lens or the vitreous humor, if the size of the illuminating source is very small.

Another example of speckle due to spatial coherence is that of displays. The spatial coherence length of modern electronic lamp projectors with a small exit pupil can be of the order of several tenths of a micrometer, which is sufficient for generating speckles on a rear projection screen made of a mi- cro-lens array for expanding the projector beam, without introducing an additional path difference

Subjective speckle pattern

in the transmitted light waves. On the other hand, no speckles appear by front projection on a scattering surface with the same projector, because, in this case, the average surface roughness of the diffusing screen is longer than the spatial coherence length of the source.

Most lasers have high temporal coherence due to their short spectral width, but also high spatial coherence, due to their small emitting aperture. The spatial coherence is greatly reduced by the scattering of an extended laser beam on a rough surface. In this case, temporal coherence plays the major role in the development of a speckle pattern of the laser illumination.

The temporal and spatial coherence of a source are not two different types of coherence, but rather different ways of interpreting the correlation function of light waves, which unify in the mutual coherence function of light waves theory,2,3 but should be kept apart in the practical explanation of speckle phenomena.

Here, only time-independent speckle patterns originating from the surface of rigid objects have been considered. If the scattering medium changes with time, the speckle pattern also evolves in time, and is known as ‘dynamic speckle’. But speckle can also be generated by random phase shifts produced by multiple scattering inside the volume of low absorbing optically diffuse materials, such as biological tissue. Since a biological material is not a rigid body and it incorporates time-varying liquid transport, spatial-time modulation of the speckle, so-called ‘bio-speckle’, is observed.

The speckle phenomenon is not only encountered by light waves, but related effects also arise in other regions of the electromagnetic spectrum, from X- rays to radio waves. Everyone using a radio receiver in a car driving at the range limit of a radio station is accustomed to the rapidly varying receiving quality, which is due to the field intensity clutters of radio waves, which correspond to speckle. In ultrasound imagery in medicine, the images are overlapped by an acoustic speckle field, which limits their contrast and resolution.

Statistical properties

In general, the statistical properties of speckle patterns depend on both the coherence of the incident light and the detailed properties of the random surface or the multiple scattering centers inside the medium. If the scattering introduces path differences greater than one wavelength and the laser is highly coherent, and a large number of scattering centers contribute to the intensity at a point in the observing plane, it can be shown that intensity I at such a point in such a speckle pattern has a negative exponential probability density function and that the probability that the intensity exceeds threshold I is given by:

Fig. 3. The probability that the intensity in a speckle field of coherent light exceeds a certain level I. The probability for incoherent light is shown for comparison.

P(I) = e-I/<I>

which is shown in Figure 3.

The ratio of the standard deviation to the mean intensity is unity for this distribution, so the contrast in the speckle pattern is equal to one. It is interesting to note that the most probable intensity at any point in such a speckle pattern is zero, and that intensities well above the mean value <I> are quite common. The intensity probability function of white light such as sunlight, which is concentrated around the mean value <I>, is shown in Figure 3 for comparison.

Another specific property of the speckle is its size distribution, or the coarseness of the granularity in the speckle pattern. The smallest diameter of speckle d is determined by the diameter of the illuminated spot and the distance z of the observer from the spot:

dmin = λ z/L

or expressed in spatial frequency:

fmax= 1/dmin = L/λz

shown in Figure 4 for a rectangular spot, with L as the side length, the distance from the spot z, and λ the illumination wavelength.

The general conclusion to be drawn from the spectrum in Figure 4 is that, in any speckle pattern, large-scale-size fluctuations are the most populous, and that no scale sizes are present beyond the small size cut-off fmax, which corresponds to a speckle

diameter of dmin.

The size of the free-space, objective speckles increases linearly with the distance from the illuminated spot. In the case of an imaging system such as the eye, the pupil can be considered a new source of randomly scattered light from a spot with a circular aperture diameter Dp and a distance z, then:

d = 1.22 λ z/Dp

46

Probability of occurrence

Fig. 4. Probability of occurrence of different spatial frequencies in a speckle pattern.

If the eye is focused on a scattering surface far away, then the image distance z is equal to the focal length f with:

d = 1.22 λ f/Dp

Since the smallest speckles imaged on the retina are only limited by the diffraction of the eye pupil, the smallest size for f = 17 mm at pupil diameter of Dp = 8 mm is d = 1.3 µm. For a pupil diameter of Dp = 2 mm, the smallest speckle diameter becomes d = 5.2 µm, which is just at the resolution limit of the eye, limited by the distance of the photoreceptors of 5 µm.

General applications

Since speckle patterns are bothersome in any kind of imagery – with laser, radar, or sound – several

T. Halldórsson

techniques have been developed in all these areas in order to dispense with them. But, on the other hand, optical speckle patterns contain valuable information about the surface of objects, and have become quite useful in metrology for the measurement of surface roughness and object deformation, which are the subjects of speckle photography and speckle interferometry.

Stellar speckle interferometry has become a valuable tool in astronomy. It is based on the fact that telescope images, blurred by atmospheric turbulence, arise from the overlap of a number of different individual speckled images, each of which containing the astronomical information mixed with that of the atmosphere fluctuation. By compensating for the speckle patterns in individual short exposure photographs, the original astronomical information can be extracted.

The measurement of dynamic speckle patterns has become an important field in speckle flowmetry in medicine for studying blood flow in biological tissue, and will be discussed further in the application of speckle on the eye in the section on Biospeckle flowmetry versus laser Doppler flowmetry below.

Deterioration of vision and methods to cure this

The presence of speckle in an image reduces the ability of a human observer to resolve the details. The spatial information present in the image, particularly in the fine details, is masked by the structure of the speckle pattern. Because of this problem, speckle noise has been an obstacle in the application of lasers in several fields, such as holographic microscopy and holographic endoscopy,

and has also been a major roadblock in the development of laser image projection and its commercial acceptability for approximately 30 years.

The severity of this problem is clearly demonstrated by measuring the contrast sensitivity function of the human eye, which is a measure of the spatial resolution capabilities of the vision system. Comparing it for coherent and incoherent illumination – with and without the presence of speckles – the overall contrast sensitivity decreases by a factor of three for lower spatial frequencies, but by a factor of 20 for a frequency of ~3 cycles/degree. It decreases overall when the pupil size decreases, because a reduction in pupil diameter signifies an increase in speckle size.4

A second problem with speckle noise is encountered in laser video color projection where monochromatic red, green, and blue laser lines are used as primary colors, and other color values are generated by a mixture of the primaries. In each image pixel on the video screen, each laser beam of the different primary colors produces an independent speckle pattern with the typical structure shown in Figure 5b, with a reference of the intensity profile of the direct beam being shown in Figure 5a.

Since the intensities of three laser beams are added inconsistently – for instance, for producing a white stimulus – the individual speckle intensity peaks for each color will cause imperfect color summation. Thus, a white laser video image consists of an average white background with a dense mask of colored scintillations of subpixel size. Of course, a critical observer will not accept such an imperfect color mix. But in a display where the image is directly scanned on the retina, this problem can be bypassed, as will be discussed below.

A number of methods has been developed to reduce speckle, which arises either from the temporal or spatial coherence of the source.5 For reducing the speckle contrast due to temporal coherence of a laser below the 1% level, its spectral bandwidth has to be increased to 8 nm, which is not possible with most lasers available today.

To reduce spatial coherence, the apparent source size has to be increased, which frequently has to be done at the cost of the transmission or resolution of the optical system.

The most successful method of reducing speckles in imaging systems, including the human eye, is to move the speckle pattern in time and, applying time averaging over a number of speckle patterns, by taking advantage of the limited integration time of cameras and the inertia of the human eye responsiveness.5 If N is the number of individual changing speckled images during the observation

time, the averaging will reduce the speckle contrast by a factor of 1/√N. A speckle pattern can be

brought into movement by different means in the optical path, by a moving light diffuser, a vibrating multimode fiber, or an acoustic modulator.6

The safest way to solve the speckle problem is to

avoid speckle. But this is only possible in imaging systems where there is no difference in the light propagation path from the source to the detecting device, the retina of the eye, or an electro-optical detector. Thus, scattering or diffracting must be omitted in the entire optical path, and only polished optical elements such as lenses and mirrors should be used.

This has been realized in the retinal laser display and the scanning laser ophthalmoscope (SLO). In both these systems, the basic principle of confocal scanning is used, where a two-axes mirror scanner moves the beam axis along a raster (xy-)pattern and is in focus on the retina. In the retinal laser display, the video information is modulated on the beam without introducing any path differences over the beam cross-section, and the size of the spot is of the order of the resolution limit of the eye itself, preventing the perception of speckle, which could be induced by the traversing of the beam through the eye medium. With the SLO, the backscattered laser light from the focused beam on the retina is imaged onto the detector aperture, which only accepts light from this tiny flying focused spot, and speckle cannot develop from the overlap of backscattered light waves from different areas of the retina because they are separated in time. Speckle due to the spatial coherence of the source can also be avoided by the correct optical design of the system.

In surgical laser applications in the eye, speckle may appear when expanded laser beams are used. In photocoagulation of the retina where a multimode fiber coupler is used between the laser and the ophthalmoscope, the number of different modes travelling through the fiber can interfere as a speckle pattern in the image of the fiber on the retina, leading to an inhomogeneous intensity distribution over an expanded beam spot. But, of course, the internal light scattering in the retinal tissue smooths this modulation. In laser keratotomy, speckle of the various spatial modes of the laser leads to an inhomogeneous intensity distribution across the beam spot applied, which also becomes unnoticed because of the intensity of the smoothing by the scanning process.

Laser speckle optometer

Since the speckle pattern of a diffuse object observed with the human eye is always in focus on the retina, irrespective of the refractive errors of the observer, it represents an ideal reference for the emmetropic, ‘rested’ eye, with its far point at infinity. Thus, speckle patterns may be used to examine the state of refraction of the eye. If a diffusing surface illuminated by coherent light far away moves perpendicular to the line of sight of an observer, the speckles may appear to move with respect to the surface. Assuming a normal eye,

movement in a direction opposite to that of the surface indicates under-accommodation, and movement with the surface indicates too strong an accommodation. If the speckles do not move, but just seem to expand or ‘boil’, the observed surface is optically conjugate to the retina.

Since its invention by Knoll in 1966,7 the laser speckle optometer has been found to be rather useful in scientific investigations on the dynamic accommodation processes of the eye, but it never became a commercial diagnostic tool because of its limitation of only being able to measure the refractive state of one monochromatic color.

Bio-speckle flowmetry versus laser Doppler flowmetry

Fluorescein angiography is a standard clinical method for the measurement of retinal and choroidal hemodynamics. However, it often only provides qualitative information, and is rather demanding in routine clinical use. Thus, some researchers have studied two alternative optical methods extensively for several years: laser Doppler flowmetry and biospeckle flowmetry. With Doppler flowmetry, the velocity-dependent Doppler frequency shift of scattered laser light by the red blood cells is evaluated. Bio-speckle flowmetry is based on measurement of the time-varying properties of speckles, depending on blood flow.

There is a fundamental difference to both approaches. The Doppler shift only appears with movement of the blood cells in a direction parallel to the axis of observation, and vanishes in a flow direction perpendicular to the axis. Since the measuring direction has to be perpendicular to the vessels in the retina, this method is limited to sensing of velocity components of the blood cells perpendicular to the direction of the main blood flow. Its accuracy thus depends on how reliable this velocity component is as a measure of the total flow velocities in the vessels, for different flow velocities and vessel sizes. Contrary to this, the fluctuation of biospeckles is independent of the observation axis.

With laser Doppler flowmetry, introduced into ophthalmology in 1972 by Riva et al.,8 the backscattered temporal intensity signal from the detector is transformed into the frequency domain by Fourier transform, resulting in the so-called power spectrum, which contains a frequency shift proportional to the blood cell velocity.

The laser Doppler flowmeter has mainly been used for localized measurements in blood vessels, but recently Heidelberg Engineering introduced a scanning laser Doppler flowmeter.9 By means of this technique, laser Doppler measurements are performed in a two-dimensional array of points, resulting in two-dimensionally resolved perfusion maps with a matrix of 256 × 64 pixels and a size of 11.2 × 11.2 µm. With laser Doppler flowmetry

at a single point, high flow velocities of up to about 100 mm/sec can be detected but, due to the much higher data rates in the scanning device, the highest measurable velocity and signal/ratio are considerably lower, or of the order of 10 mm/sec.

With bio-speckle flowmetry, compared to laser Doppler flowmetry, the blood-flow direction and scattering geometry have no direct effect on the speckle fluctuations. Fercher et al.10 have proposed a method for visualizing the retinal blood-flow using single-exposure speckle photography, which provides a blood circulation map. However, since the photographic process is troublesome for clinical use, Aizu et al.11 proposed a method for measuring speckle fluctuation with an electronic detector, obtaining the blood rate by analyzing the power spectrum of the speckle intensity fluctuations in the image plane. Later on, Aizu et al.12 improved their technique by measuring the photon correlation in the diffraction (Fourier) plane. This method evaluates the overall activity of various blood flows existing in the illuminated area, rather than the absolute flow velocity at a certain point in a single vessel.

For 2-D mapping of flow velocities by monitoring speckle fluctuations similar to those with the scanning laser Doppler flowmeter – but without the need of scanning – measurements of the image contrast of speckles have been used. The intensity fluctuations of the speckles due to the blood flow blur the speckle pattern, and hence reduce its contrast. With a suitable integration time for the exposure, velocity can be mapped as speckle contrast.

Konishi and Fujii13 described a bio-speckle flowmeter known as ‘laser flowgraphy’, where the ‘blur’ value is measured in a hard-wired circuit in a matrix of 100 × 100 pixels, with a pixel size of 25 × 25 µm and a rate of 600 frames/sec. The series of 2-D maps taken at 16 frames/sec clearly visualizes the pulsation of the blood flow.

Briers and Xiao-Wei14 described a further development in the data processing for this technique, using a CCD camera and a framegrabber to capture an image of the area of interest. The local speckle contrast is computed and used to produce falsecolor map of velocities. The results are similar to those obtained with the scanning laser Doppler technique, but are obtained without the need of scanning. This reduces the time needed for capturing the image from several minutes to a fraction of a second, already a clinical advantage.

Conclusions

The principles of the speckle phenomenon depend upon the wave-nature of light and follow laws of interference of light. The measurement of dynamic speckle patterns has become an important field in speckle flowmetry. With bio-speckle flowmetry, compared to laser Doppler flowmetry, the blood-

flow direction and scattering geometry have no direct effect upon the speckle fluctuations. Konishi et al. have described a bio-speckle flowmeter known as the ‘laser flowgraph’.

References

1.Newton I: Opticks (reprinted by Dover Press, New York, NY, 1952) Book I, Part I, Prop. VIII, Prob. II., 1730

2.Goodman JW: Statistical Optics. New York, NY: John Wiley & Sons 1985

3.Dainty JC (ed): Laser Speckle and Related Phenomena, Topics in Applied Physics, 9. Berlin/Heidelberg: Springer Verlag 1984

4.Artigas JM, Felipe A, Buades MJ: Contrast sensitivity of the visual system in speckle imagery. J Opt Soc Am 11:23452349, 1994

5.Iwai T, Asakura T: Speckle reduction in coherent information processing. Proc IEEE 84:765-781, 1996

6.Wang L, Tschudi T, Boeddinghaus M, Elbert A, Halldórsson T, Pétursson P: Speckle reduction in laser projections with ultrasonic waves. Opt Eng 39:1659-1664, 2000

7.Knoll HA: Measuring ametropia with a gas laser. Am J Optom Arch Am Optom 43:415-418, 1966

8.Riva CE, Ross B, Benedk GB: Laser Doppler measure-

ment of blood flow in capillary tubes and retinal arteries. Invest Ophthalmol Vis Sci 11:936-944, 1972

9.Zinser G: Scanning laser Doppler flowmetry: principle and technique. In: Pillunat LE, Harris A, Anderson DR, Greve EL (eds), Current Concepts on Ocular Blood Flow in Glaucoma. pp. 197-204. The Hague: Kugler Publications 1999

10.Fercher AF, Peukert M, Roth E: Visualization and measurement of retinal blood flow by means of laser speckle photography. Opt Eng 25:731-735, 1986

11.Aizu Y, Ogino K, Koyama, T, Takai N, Asakura T: Evaluation of retinal blood flow using time-varying laser speckle. In: Adrian RJ (ed) Laser Anemometry in Fluid Mechanics. III. pp. 55-68. Lisbon: Ladoan 1988

12.Aizu Y, Ogino K, Sugita T,Yamamoto T, Takai N, Asakura T: Evaluation of blood flow at ocular fundus by using laser speckle. Appl Optics 31:3020-3029, 1992

13.Konishi N, Fujii H: Real-time visualization of retinal microcirculation by laser flowgraphy. Opt Eng 34:753-757, 1995

14.Briers JD, Xiao-Wei H: Laser speckle contrast analysis (LASCA) for blood flow visualization: improved image processing. In: Priezzhev AV, Asakura T, Briers JD (eds) Proceedings SPIE, Vol 3252, Optical Diagnostics of Biological Fluids III. pp. 26-33. The International Society for Optical Engineering, Washington DC, 1998

Introduction

The measurement of blood flow in the ocular fundus is of scientific, as well as of clinical, interest. Its scientific value lies in the possibility of gaining insight into the physiology of deep vascular beds that are under local and central nervous control. Its clinical potential lies in the early assessment of alterations in blood flow, whether associated with specific ocular diseases or resulting from systemic ailments. Furthermore, evaluation of the effect of treatment on the disturbed blood flow represents an important area of application of such a measurement.

Ideally, in order to be clinically applicable, blood flow measuring techniques should be reproducible, accurate, and sensitive enough to be able to reveal early pathological alterations. Their spatial resolution should permit measurements at discrete sites of the retinal, optic nerve, and choroidal vascular systems. Their temporal response should be fast enough to allow the investigation of blood flow regulatory responses evoked by various physiological stimuli.

The advent of the laser, a device that emits optical waves of almost single frequency, has made it possible to detect, with extremely high resolution, the Doppler shift that light undergoes when scattered by a moving particle. This has allowed the measurement of a broad range of velocities (from µm/s to many km/s). In 1972, this capability led to the first report on the application of the Doppler effect to the measurement of blood velocity, which was obtained from a rabbit retinal arteriole using a helium-neon laser.1 In 1974, Tanaka et al. published the first laser Doppler velocimetry (LDV) measurement of blood in retinal vessels of human

volunteers.2 After the pioneering article by Stern,3 who proposed examining the hemodynamics in the tissue of the skin using LDV, Riva et al.4 described a method to measure blood velocity in the human optic nerve microcirculation. This method was then extended to measuring blood flow by laser Doppler flowmetry (LDF) in the vascular bed of the cat optic nerve head (ONH),5 human ONH6,7 and subfoveal choroid.8 In 1995, Michelson and et al.9 first reported LDF mapping of blood flow in the microcirculation of the human retina by means of a scanning laser ophthalmoscope.

Due to the limitations of the space and scope of this review, the present chapter is by no means an exhaustive description of LDV and LDF. Regrettably, numerous important LDV and LDF studies could not be cited. Part of the material in this chapter has been reproduced with permission from previous publications.7,10,11 First, we will describe the LDV technique for measuring blood flow in the main retinal vessels and will discuss some recent developments. Then, the principle of LDF for the measurement of red blood cell (RBC) flux in the tissues of the ONH, subfoveal choroid, and iris will be introduced and applications discussed.

The Doppler effect

The basis of LDV and LDF is the Doppler effect first described in 1842 by the Austrian physicist Christian Doppler in an article entitled On the Colored Light of Double Stars and Some Other Heavenly Bodies, which describes the frequency shift that a sound or light wave undergoes when emitted from an object that is moving away or towards an observer. It manifests itself, for example,

Fig. 1. The Doppler effect. The frequency of the light scattered by the particle (velocity V) in the direction defined by αs is shifted in frequency by an amount ∆f compared to that of the incident light ( fi) from the direction defined by αi (see text for explanation). (Adapted from Riva and Petrig11 by courtesy of the Publisher.)

in the increase in the pitch of the siren of an approaching ambulance.

Consider a single particle such as an RBC moving at velocity V in the direction shown in Figure 1. A laser beam of single frequency fi is incident to this particle at an angle αi to the direction of V. The incident light is scattered by the particle in various directions. In the direction of the detector, defined by the angle αs, the frequency of this light will differ from fi by an amount ∆f equal to

∆f = V (cos αs – cos αi) n / λ

which is the so-called Doppler shift. Its magnitude depends upon V, αs and αi, the index of refraction n of the medium containing the particle and the wavelength λ of the laser light in vacuo. For a particle moving at a speed of 1 cm/s, with αs = 80°, αi = 90°, n = 1 (air), and λ = 632.8 nm (heliumneon laser), ∆f is equal to 2.7 × 103 Hz. Although extremely small compared to fi (~5 × 1014 Hz), this shift can be detected using optical mixing spectroscopy.12

Laser Doppler velocimetry measurements of blood velocity in individual retinal vessels

Doppler shift power spectrum for RBCs moving in individual retinal vessels

Particles suspended in a fluid moving at constant mean velocity through a tube (particles much smaller than the tube diameter) have velocities that depend upon their radial position in the tube. With Poiseuille flow (Fig. 2A), for example, the distribution of velocities as a function of radial position has a parabolic shape, with the peak velocity at the center and zero velocity at the wall. To this distribution of velocities, a spectrum of Doppler shifts corresponds, the so-called Doppler shift power spectrum (DSPS). In our model (Fig. 2B), the DSPS extends from ∆f = 0, which corresponds to the velocity of the particles at the wall of the tube,

to ∆f = ∆fmax, where ∆fmax is the frequency shift arising from the particles moving with the center-

line velocity, Vmax. ∆fmax is the ‘cutoff frequency’

of the DSPS. Furthermore, if the particles are uniformly distributed across the tube, it can be shown that the DSPS is constant from ∆f = 0 to ∆f = ∆fmax.13 ∆fmax is measured using the autodyne mode of optical mixing spectroscopy. A description of this technique is beyond the scope of this paper and the interested reader is referred to a previous publication.14

Using bidirectional LDV, an absolute measurement of Vmax can be obtained by detecting the scattered light along two scattering directions, and determining the DSPS for each direction.15 Vmax (cm/s) is derived from the cutoff frequencies ∆fmax1 and ∆fmax2 through the relation

Vmax = k (|∆fmax1 – ∆fmax2|).

The constant k depends upon the intraocular angle between the two scattering directions, the index of refraction of the ocular media, and the wavelength of the incident laser beam, all of which are known.

Retinal blood flow through a retinal vessel is

defined as Q = S × Vmean, where S = π D2/4 is the cross sectional area, D the diameter of the vessel

and Vmean the mean blood velocity. D is usually measured from fundus photographs taken in mono-

chromatic light at around 570 nm in order to obtain maximum contrast of the blood column relative to the background. The accuracy of Q depends upon

that of Vmax and D2, and therefore, it is twice as sensitive to the accuracy to which D can be mea-

sured. The relationship between Vmean and Vmax depends on the velocity profile. For a parabolic profile, Vmean = Vmax / 2.

Instrumentation

A bidirectional retinal LDV device consists of optical systems (i) to deliver a laser beam to a given

site on a retinal vessel; (ii) to collect the light scattered by the RBCs along two directions; and (iii) to allow observation of the fundus by an operator. In addition, there is a fixation target for the subject to reduce eye movements. Bi-directional laser delivery and detection systems have been incorporated into a slit-lamp microscope15,16 and into various fundus cameras.17,18

Electronics and signal processing

The light detector transforms the incident laser light into an electrical current (photocurrent) signal, which is further processed by electronic filtering and amplification. This resulting so-called ‘Doppler signal’ contains the sum of the Doppler shift components from all moving RBCs. These signal components are separated from each other using fast Fourier analysis, followed by power spectrum estimation. The resulting DSPS is essentially the histogram (distribution) of signal power as a function of Doppler shift frequency (Figs. 2B and 5). Depending on the type of application (LDV or LDF), the DSPS is evaluated by different means of curve fitting models19 and statistical analysis20 in order to derive the various flow parameters described in this review.

Applications of laser Doppler velocimetry

Physiology

Some of the findings obtained in normal volunteers have provided new insight into the physiology of the retinal circulation. For example, they demonstrated high temporal resolution recordings of the pulsatile time course of RBC velocity in retinal vessels (Fig. 3),15,19,21,22 and established the rela-

tionship of Vmean versus D and of Q versus D.23 Q was found to increase with D2.76 for arteries and

D2.84 for veins. This is in good agreement with the values predicted by Murray’s law,24 which stipulates that Q varies as D3 for a vascular system that minimizes its resistance for a given blood volume.

The LDV technique is particularly suitable for investigating retinal blood flow regulation in response to various physiological stimuli. These include acute increases in mean ocular perfusion pressure (PPm) achieved using isometric exercises,25 decreases in PPm induced by increasing IOP,26 increases in arterial oxygen and carbon dioxide tension,27 and light/dark transitions.28-31

Clinical applications

A number of LDV studies have led to a better understanding of the effect of diabetes on the retina. These examined (i) the retinal circulatory changes during the natural history of diabetes;32,33 (ii) the effect of poor glycemic control on retinal hemodynamics;34 (iii) the response of retinal blood flow to hyperoxia in patients with various degrees of retinopathy;35 and (iv) the effect of various treatment modalities, such as panretinal laser photocoagulation.36,37 Some of the most important LDV findings obtained in diabetic patients have been reviewed by Grunwald and Riva.38

The effect of various antihypertensive medications on the retinal circulation and its autoregulation in normal volunteers and patients with ocular hypertension and primary open-angle glaucoma have been investigated by Grunwald and col- leagues.39-41

Recent developments

As mentioned above, the relationship between Vmean and Vmax depends upon the velocity profile of the RBCs. In various situations, such as at sharp bends, arteriolar branchings, venous junctions,42 arteriovenous crossings, and impending or partial vessel occlusions, this profile deviates from the parabolic shape.43 Recently, methods have been developed to determine this profile, because a measurement of the RBC velocity profile could be of help in the early diagnosis and treatment of various retinal circulatory impairments. In particular, determination of the velocity gradient at the vessel wall could provide valuable information on the wall shear rate, a quantity that plays an important role in the control of blood flow.44,45

The technique of ‘color Doppler optical coherence tomography’ (CDOCT) allows cross-sectional imaging of blood flow.46 In CDOCT, laser light of low coherence scattered by the RBCs is made to interfere with a strong reference beam from a retroreflector external to the eye. Figure 4A shows a flow profile obtained from a 176-µm retinal vessel using CDOCT.46

Fig. 4. A. Depth-resolved velocity profile of RBCs in a 176µm diameter vessel in an undilated human eye. The profile was detected and digitized in 10.3 msec and thus does not exhibit any effects of the pulsatile nature of the flow. (Reproduced from Yazdanfar et al.46 by courtesy of the Publisher.) B. Velocity profile obtained from a 150-µm retinal vein of a human eye by scanning a 670-nm coherent laser beam across a straight portion of the vessel.48

Using lasers with different coherence lengths to obtain Doppler shifts from RBCs moving in various volumes of increasing depths from the vessel wall provides another approach to monitor in vivo the velocity gradient at the vessel wall.47 With this ‘variable coherence optical Doppler velocimetry’ (VCODV) only the light from RBCs moving at a depth of less than half the coherence length is efficiently detected. Yet another technique for measuring the RBC velocity profile consists of scanning a 12-µm diameter coherent laser beam perpendicularly across retinal vessels.48 Such scans have demonstrated a parabolic shape of the velocity profile in straight portions of retinal vessels (Fig. 4B).

Laser Doppler flowmetry measurements of blood flow in the optic nerve head, subfoveal choroid and iris

The Doppler shift power spectrum in the case of red blood cells moving in the microvascular bed of a tissue

When a laser beam illuminates RBCs moving through a network of capillaries at various velocities and in different directions, the light scattered by the RBCs consists of a summation of waves with various Doppler shifts ∆fi. It can be generally noted that: (i) Most of the light emerging from the tissue has been scattered solely by static structural components of the tissue. This non-shifted light acts as a reference signal that is mixed with the shifted scattered light at the surface of the photodetector. The photocurrent contains only the components oscillating at the Doppler shift frequencies (∆fi). (ii) The light scattered by the RBCs contains Doppler shift frequencies that can be positive or negative, depending on the direction of RBC motion relative to the incident light and detector. Since the detector does not discriminate between positive and negative frequency shifts, the DSPS only spans the positive frequencies (Fig. 5).

Fig. 5. DSPS of the optic nerve tissue. Arrow indicates the mean frequency, which is proportional to the mean velocity of the RBCs. (Reproduced from Riva and Petrig11 by courtesy of the Publisher.)

Hemodynamic parameters derived from the Doppler shift power spectrum

Assuming the validity of Bonner and Nossal’s theory,49 the following flow parameters are obtained from the DSPS. Vel is the mean speed of the RBCs moving in the sampling volume (proportional to the mean Doppler frequency shift). Vol is the number of moving RBCs in the sampling volume (proportional to the area under the DSPS curve). The total RBC flux in the sampling volume is F = Vel × Vol, where Vel is expressed in Hz, and Vol and F in arbitrary units.

This means that the LDF technique provides only relative blood flow measurements for the following reasons. Laser radiation upon a tissue will undergo scattering and absorption, both influencing the penetration pattern of the laser light. Penetration may differ from one region of a tissue to another, depending upon the optical properties of the tissue. Thus, spatial or temporal variations in tissue structure and vascularization, as is the case, for example, in the ONH in glaucoma, will affect the LDF measurements. Furthermore, direct comparison between the flow values from different tissues may not be valid due to variations in optical properties resulting from differences in tissue structure and composition.

The measured quantity F is usually referred to as ‘blood flow’. However, what is actually measured is the flux of the RBCs. Blood flow is only directly proportional to RBC flux if the hematocrit remains constant during an experiment.

Laser Doppler flowmetry measurement modes

Two LDF measurement modes have been implemented. The first is the continuous mode for online, continuous recording of the flow parameters at a discrete site of the vascular beds of the ONH, subfoveal region of the choroid, or iris. The second mode is based on a scanning laser technique and provides a two-dimensional image of the RBC flux in the capillaries of the ONH and retina.

Continuous recording of the laser Doppler flowmetry signal in the optic nerve head and subfoveal choroid

In ONH LDF, as originally described by Riva et al.,5 an optical system adapted to a standard fundus camera delivers a laser beam to a discrete site on the optic disc. The scattered light is collected by an optical fiber placed in the retinal plane of the camera and guided to a photodetector. An area of the fundus (30° in diameter) is illuminated in red-free light, allowing the observation and positioning of the laser beam at the disc, away from visible blood vessels. The effective diameter at the disc from which the scattered light is collected is approximately 150 µm.

A NeXT computer system with dedicated software is used for the LDF analysis.20 This software allows averaging of the Doppler signal in phase with the heart cycle so that precise measurements of RBC flux variations during the systolic and diastolic phases can be obtained. Recordings of Vel, Vol and F from the ONH of a normal volunteer are shown in Figure 6.

Scanning laser Doppler flowmetry

Scanning laser Doppler flowmetry (SLDF) combines the techniques of LDF and scanning laser ophthalmoscopy.50,51 It is based on the principle of

confocal microscopy and has a nominal depth resolution of approximately 300 µm. The Heidelberg Retinal Flowmeter (HRF) performs quick measurements at 16,384 different locations in a two-dimensional grid, and provides an image of the retinal perfusion. The perfusion map can be used for a qualitative visualization of the network of perfused vessels and capillaries. It is also possible to define a measurement region of variable size (a 100 x 100 µm window is commonly used), to place it interactively anywhere in the perfusion map, and to measure the average perfusion values inside this region. This technique is limited to the detection of Doppler shifts below 2000 Hz.

Laser Doppler flowmetry sample volume

A central question in the application of LDF to the ONH is the depth of the sampling volume. This depth determines the relative contribution to the Doppler signal of the superficial layers, those supplied by the central retinal artery, and the deeper layers supplied by the posterior ciliary arteries. These two vascular beds may have different blood flow regulation properties. Furthermore, the deep layers of the ONH appear to be particularly susceptible to ischemic disorders, including glaucoma.

Investigations on a model system suggests that, when the light-collecting aperture coincides with the tissue volume illuminated by the probing laser, layers of the ONH tissue of as deep as 300 µm contribute to the LDF signal.52 In humans, however, although the depth of tissue sampling in the ONH remains to be experimentally assessed, it appears that the LDF technique detects predominantly the motion of RBCs within the intraocular region of the ONH.53 A study on monkey eyes54 concluded that LDF is predominantly sensitive to blood flow changes in the superficial layers of the ONH, and less to those layers of the prelaminar and deeper regions of the ONH, and that their relative proportions are still unknown. The weaker signal from the deep layers cannot be separated from the dominant signal from the superficial layers to exclusively study the circulation in the deep layers.

Linearity of laser Doppler flowmetry

Linearity between F and actual blood flow has been documented for various tissues, such as the skin, skeletal muscle, cerebral cortex, nerves, etc.55 Experiments have shown that the assumption of LDF linearity is valid for the ONH and choroidal circulations.8,11

Applications of laser Doppler flowmetry

The high spatial and temporal resolution of the LDF technique, particularly in the continuous mode, makes this technique most suitable for investigation of the regulatory processes of blood flow in response to various physiological stimuli.

Optic nerve head

LDF investigations of ONH blood flow in humans include the response of this flow to: (i) decreases in PPm induced by increases in IOP;53,56 (ii) increases in PPm produced by increases in systemic blood pressure with isometric exercises;57 (iii) hyperoxia, breathing carbogen and mixtures of O2 and CO2; and (iv) increased neuronal activity (Fig. 7).15,61

LDF and SLDF have been used to measure retinal and ONH microvascular perfusion in normal, ocular hypertensive, and glaucomatous eyes, under various clinical conditions and using different provocation tests. Other clinical investigations include the study of retinal vein occlusions67 and retinal blood flow in age-related macular degeneration.51,68

Choroid and iris

LDF measurements of choroidal blood flow in the foveal region of the human fundus are recent. Studies have been performed in humans on the effect of: (i) increases and decreases of PPm;69,70 (ii) valsalva maneuvers;8 (iii) breathing of various gas mixtures (pure O2, various mixtures of O2 and

CO2);71 and (iv) the effect of light.72 Investigations on the effect of aging, age-related macular degeneration, and choroidal neovascularization have been reported.73,74

LDF has been applied to investigate iris blood flow in humans, as well as the effect of acute physical exercise75 and increased IOP76 on this flow.

Conclusions

The LDV and LDF techniques have been applied over a number of years. They are powerful methods for noninvasively investigating changes in blood flow in the retina, ONH, subfoveal choroid, and iris. Both techniques have high sensitivity and a temporal response fast enough to reveal the changes in blood flow during the cardiac cycle, and in response to acute changes in various physiological stimuli. These capabilities open new avenues in the understanding of the regulation of blood flow in the various tissues of the eye.

Acknowledgments

The authors wish to thank Martial Geiser for his help in preparing the manuscript and Eric Logan for providing figure 4B. This study was supported in part by the Swiss National Science Foundation (Grant No. 32-43157), the Priority Program ‘Optics II’ (Grant No. 491), the EMDO Foundation, Ciba Vision Ophthalmics, the Mobilière Suisse, and the Loterie Suisse Romande.

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