Ocular microtremor measurement using laser-speckle metrology

Emer Kenny; Davis Coakley; Gerard Boyle

doi:10.1117/1.JBO.18.1.016010

11 January 2013 Ocular microtremor measurement using laser-speckle metrology

Emer Kenny, Davis Coakley, Gerard Boyle

Author Affiliations +

Journal of Biomedical Optics, Vol. 18, Issue 1, 016010 (January 2013). https://doi.org/10.1117/1.JBO.18.1.016010

Abstract

We describe a novel, noninvasive measurement approach for recording a small involuntary tremor of the eye known as ocular microtremor. The method is based on measuring out-of-plane angular displacements of a target by using laser-speckle correlation of images recorded in the Fourier plane of a lens. The system has a dynamic range of 4 to 5000 μrad, resolution of 4 μrad, and a bandwidth of 250 Hz. The design and optimization of the system is presented with an in vitro validation of the system against its specification.

1. Introduction

Fixational eye movements are present in all subjects even when the eye appears to be at rest. These fixational movements are composed of three types of involuntary eye movements: microsaccades, drift, and ocular microtremor (OMT).¹^,²

OMT is the smallest of the involuntary eye movements. It has an amplitude range of 150 to 2500 nm (12 to 216 μrad rotational) peak-to-peak, with a typical amplitude of 1 μm (87 μrad). The frequency range of OMT is between 20 to 150 Hz with an average peak frequency of 84 Hz³ for a normal subject. It is a nonperiodic, continual, high-frequency, wave-like physiological tremor.⁴^,⁵ Microtremor occurs simultaneously with drift, which is a slow, continuous irregular movement that takes place between the more rapid and intermittent microsaccades.

Clinical use of OMT has been investigated in coma,⁶ MS,⁷ Parkinson’s disease,⁸ and depth of anaesthesia.⁹^,¹⁰ Recent studies have attempted to understand the particular role of OMT in vision.¹¹ It is believed OMT arises from brainstem neurons.⁵^,¹²^,¹³

Most measurements of OMT to date have relied on an eye-contacting probe method.¹⁴^,¹⁵ Drawbacks of these probes include the requirement to anaesthetise the eye, inter-observer variability, probe influence on the measurement result and patient discomfort.¹⁶^,¹⁷

Despite its potential, a full understanding of OMT is incomplete due to the absence of a device to measure it noninvasively. For practical clinical use, a noncontacting method for OMT measurement would be most suitable. Ideally the device would be of a high resolution yet robust enough to measure OMT in a clinical environment. Boyle et al.¹⁸ proposed a speckle interferometry method for noncontact measurement of OMT from the eye sclera. The system achieved a resolution suitable for OMT measurement, though the setup was difficult to implement due to the bulk optics utilized. A promising outcome of the work by Boyle was that it showed the sclera to be an appropriate surface for measuring OMT using speckle-based methods. As a continuation of the work by Boyle, Ryle et al.¹⁹ developed a speckle interferometry OMT measurement system using laser diodes in order to reduce the physical size of the system. However, again the system was difficult to implement.

Here we investigate the feasibility of using laser-speckle correlation to track OMT from the surface of the sclera and outline the requirements for such a measurement system. Specifically, we investigate the application of a laser-speckle technique using Fourier plane imaging to measure OMT. The technique potentially presents advantages over other optical eye-movement measurement techniques in terms of resolution, ease of setup, and robustness to misalignment. To our knowledge this approach has not been applied previously to eye-movement measurement and would represent an important addition to the relatively limited number of noncontact eye movement techniques available,²⁰^,²¹ if its utility can be demonstrated. While the basic optical technique has been described elsewhere, it has been validated and applied only for the measurement of relatively simple displacements of inanimate objects, such as small rotation of metal shafts. The eye presents a much more challenging target. To adapt and validate the technique for OMT measurement requires the issues of eye safety, background eye movement, and biospeckle to be resolved. The former two issues are addressed in this paper, as moving to investigate biospeckle effects in vivo initially requires the basic technique to be proven in vitro at eye safe power levels against the known motion of a target. To address eye safety, we implement the technique here at much lower laser power levels than have been used previously and utilize a high-sensitivity electron multiplying charged couple device camera to attempt to compensate for the consequent drop in signal and potential loss of resolution. OMT takes place against a background of “contaminating” background eye and head movements. A downside of the fundamental optical technique used here is that it is vulnerable to failure through decorrelation effects for “large” movements. A series of validation tests are presented here to realistically challenge the proposed measurement approach and to determine if it can be configured to resolve the very low-amplitude rotations caused by OMT, despite the necessary restrictions on laser power and the presence of larger amplitude background motion.

1.1.

Measurement Requirements

The reported amplitude of OMT varies in the literature. For metrology purposes, most OMT measurements that have been recorded using the contacting probes method give the amplitude in terms of nanometers. For our purposes, we convert these figures to units of angular rotation of the eye by noting that 87 μrad is equivalent to a 1 μm displacement for a typical eye diameter of 23 mm.

1.1.1.

Frame rate

The frame rate of a camera attempting to capture speckle moving at OMT frequencies must obey the Nyquist sampling theorem. To do this, the sampling frequency ( $f_{s}$ ) must be greater than or equal to twice the highest frequency contained in the signal, i.e., for OMT measurement the frame rate must be $\geq 2 (150 Hz)$ . In the case of living tissue such as the eye, biospeckle will be present in the signal captured by the camera. At present, the rate of biospeckle motion in the eye is unknown, and so a higher sampling frequency than that required for OMT alone would be beneficial. A frame rate of 500 Hz (500 frames per second) is high enough to obey the Nyquist theorem and avoid aliasing of the OMT signal.

1.1.2.

Dynamic range and resolution

Generally a dynamic range of 2 to 216 μrad (25 to 2500 nm peak-to-peak) and system resolution of 2 μrad has been found to be adequate to track the OMT signal.¹⁵^,¹⁶^,¹⁸ Although this dynamic range is sufficient to capture OMT, when a large intermittent microsaccade or other movement occurs, a momentary saturation arises in the measurement. More recent studies have used a dynamic range of 2 μrad to9.52 mrad (25to 110 μm)¹¹^,²² so that other fixational movements could also be recorded. In a contacting probe measurement system, the system dynamic range and resolution are critical parameters.

In a speckle correlation system, dynamic range will be determined by the maximum allowable frame displacement relative to a reference frame taken at the start of the measurement. A large frame-to-frame displacement will cause a decorrelation in the measurement and reduce the accuracy. Some intermittent resetting of the reference frame could be tolerated in response to large movements. This would be apparent as a discontinuity in the measured movement trace. However, at a minimum, the system needs to tolerate the expected frame-to-frame displacement. Therefore some a priori knowledge of estimates for how large these displacements might be is needed in order to design a system capable of measuring OMT against a background of other movements.

1.1.3.

Influence of other eye movements on measurement

Other eye movements can lead to decorrelation of the speckle correlation images. Table 1 displays the amplitude, frequency, and velocity ranges estimated from the literature for each of the fixational eye movements. Drift and microsaccades have an amplitude of about 290 μrad and 1.45 mrad, respectively. Drift has a frequency of 2 to 5 Hz and, as previously mentioned, occurs simultaneously with OMT. Microsaccades are more rapid and sporadic and occur approximately twice every second. An imaging system recording speckle from the eye would capture the net displacement of the eye surface resulting from all three fixational movements. Post processing of the images must therefore include a filtering method to separate the OMT signal from the other eye movements.

Table 1

Characteristics of the fixational eye movements. Velocity measurements are based on the amplitude and frequency (unless referenced).

	Amplitude (μrad)	Frequency (Hz)	Maximum velocity ( $m rad / s$ )	Maximum rotation per frame at 500 FPS ( $μ rad / frame$ )
OMT	12 to 200 peak to peak	$\sim 80$	50	101
Drift	290	2 to 5	9²	18
Microsaccade	1450	1 to 2	637²	1274

Table 2

Characteristics of other body movements that may influence OMT. Velocity measurements are calculated based on the amplitude and frequency.

	Amplitude (mrad)	Frequency (Hz)	Maximum velocity ( $m rad / s$ )	Maximum rotation per frame at 500 FPS ( $μ rad / frame$ )
Headrest	9²³	2 to 3	85	170
Hand	4 to 17¹⁶^,²⁴	7 to 12	641	1282

1.1.4.

Influence of body movements on measurement

Unwanted head movements can occur during eye-movement measurement. These can have a negative influence on the accuracy of measurements since the eye globes participate in the compound movements of the head. Natural functions such as breathing and heart rate can affect these head movements. Head movements vary in amplitude between measurements and between subjects, and so it is difficult to establish their amplitude. Table 2 displays the amplitude, frequency, and velocity ranges estimated from the literature for each of the unwanted head movements. To stabilize the head while recordings are being taken, a headrest may be used. It has been shown, however, that standard ophthalmic headrests do not eliminate all head movement and amplitudes in the range of $\pm 9 mrad$ ( $\pm 100 μ m$ ) at 2 to 3 Hz are still possible with their use.²³

In a clinical environment, a portable handheld measurement device would be the ideal solution in cases where the patient is not mobile and cannot place his own head in a headrest. Shaking of the hands while holding the device would add additional noise to the system. The outstretched arm has a natural tremor of 4 to 17 mrad (50 to 200 μm) in amplitude with a frequency of 7 to 12 Hz.¹⁶^,²⁴

1.1.5.

Required frame-to-frame measurement ability

In order to determine the required frame-to-frame measurement ability of the system, the likely displacement per frame of all movements that may influence the OMT signal must be calculated. It is clear that in a headrest device, the dominant components are likely to be microsaccades. Treating the above velocities as vectors, the maximum possible angular velocity will occur for a situation where all velocities are in the same direction. In this case, the maximum velocity would be

(OMT + drift + microsaccades + head) = (50 + 9 + 637 + 85) mrad = 781 mrad / s .

At our proposed frame rate of 500FPS, the maximum possible displacement per frame is estimated to be 1.56 mrad.

Including motion from a handheld device the maximum velocity would increase to $1422 mrad / s$ and the maximum possible displacement per frame would increase to 2.84 mrad. From these figures, it is apparent that hand movement would become the dominant motion in a measurement system. The velocity and displacement of the total movements almost double when hand movement is included. At present, the measurement device is table mounted and so further calculations will be derived for a non-handheld device.

The unwanted eye, head, and hand movements have frequencies below that of OMT, and so a filter may be implemented to remove them with signal processing. The filtering process would not work however if the frame-to-frame decorrelation caused by the head and hand movements is large. The effects of this possible decorrelation must therefore be investigated and quantified.

In summary, the following parameters are required for an OMT speckle correlation measurement system: (1) a resolution of 2 μrad; (2) a dynamic range of 2 μ to 9.52 mrad; (3) a frame rate of 500FPS; and (4) a minimum frame-to-frame measurement ability of 1.56 mrad.

1.2.

Fourier Plane Measurement Technique

Figure 1 shows the arrangement used by Rose et al.²⁵^,²⁶ for angular speckle displacement measurement. Light from a collimated laser beam is directed through a beam splitter to a target where it is then reflected back to an image sensor placed in the Fourier plane (i.e., $z_{2} = f$ ) of a lens with aperture $σ$ . The out-of-plane angular rotation ( $θ$ ) of the object is transformed to a linear displacement ( $p_{x}$ ) in the Fourier plane of a lens. An image sensor placed in the Fourier plane records the speckle patterns over a certain time. The speckle images are then post-processed using digital-image correlation to measure the linear displacement between speckle images. This linear displacement is then converted to angular rotation of the object using the simple equation²⁵

Eq. (1)

θ = \frac{p_{x}}{2 f} .

Fig. 1

Setup for Fourier plane measurement technique.

Speckle techniques recorded in the imaging plane are dependent on a number of variables such as the lens focal length, working distance, numerical aperture, the wavelength of the light, and the target shape. An advantage of the Fourier technique implemented by Rose et al.²⁶ is that the angular displacement is dependant only on the linear speckle image displacement and on the lens focal length ( $f$ ), hence the setup of the system is much less stringent than that of an imaging plane technique.

Other advantages in terms of precise OMT measurement with this technique are the proven range and sensitivity that can be achieved. In their paper, Rose et al.²⁶ report a resolution of 5 μrad for the technique; this is close to the ideal OMT system resolution of 2 μrad. Further, the method has been proven to be insensitive to target shape and to target distance ( $z_{1}$ ).The latter is important to OMT measurement, since it would allow for simple setup of the equipment without a rigid working distance. A fundamental advantage of the technique designed by Rose et al.²⁶ is that their system is sensitive only to rotation. This is significant for OMT measurement as it would imply that the method is robust and insensitive to any left/right or back/front motion of the subject as the measurement is being taken.

1.3.

Design Parameters

Using the Rose method, as described above, there are only three variables in the setup: the beam radius $r_{s}$ , lens focal length $f$ , and lens aperture $σ$ . In the following section, the influence of these parameters on the design of the system will be discussed with an aim to find optimized values for an OMT measurement system and to calculate the theoretical dynamic range of our system. Laser power constraints due to eye safety are also discussed.

Due to the low light levels in this experiment, it would be prudent to use a smaller focal length lens in order to keep the target-to-lens-to-camera-sensor distance shorter and hence collect more reflected light at the sensor. An $f = 150 mm$ lens was considered to be a good compromise between achievable resolution and reflected intensity, reducing the estimated resolution to 4 μrad.

To achieve a speckle size that is at least as large as one pixel, using a focal length of $f = 150 mm$ as derived above, the beam radius must not be larger than 1.26 mm for a 632.8-nm laser.

Using the lateral sclera as a target, the beam diameter must be able to fit within the accessible space on the sclera. For a typical adult eye, the available space is approximately 4 mm. Therefore a beam radius of up to 2 mm would fit on the sclera.

A small beam radius is desirable because it will provide a higher signal-to-noise ratio and a higher speckle size. For this reason, we opted not to adjust the actual beam radius of the laser used in this experiment and the given radius was 0.6 mm. This beam radius is well within the available space on the sclera.

Using the theory outlined in Rose et al.²⁵^,²⁶ and assuming fully developed speckle, to achieve a decorrelation factor of 0.9 or higher for a maximum possible angular displacement of $θ = 1.56 mrad$ (as derived in Sec. 1.1) with a lens focal length of $f = 150 mm$ , then the lens aperture must be greater than or equal to 2.04 mm. For our setup, we chose a standard optic size of 25 mm.

Large movements will decorrelate images from frame-to-frame. This will have an impact on the dynamic range. The ceiling on the dynamic range achievable by the system can be determined using Eq. (1). From this, the angular displacement required to translate a single speckle across the image sensor can be calculated. For a lens focal length of 150 mm and a $128 \times 128$ image sensor with a 24 μm pixel pitch the angular displacement required to displace one speckle fully across the sensor is 10 mrad. Therefore, in a scenario where each frame is correlated with an original undisplaced reference frame, the theoretical maximum achievable dynamic range for our system is 10 mrad.

The laser power used in an OMT measurement system must be restricted to a safe level and yet be high enough to achieve a reasonable signal-to-noise ratio at the imaging detector. Ideally the laser light would be visible so that alignment of the laser with the eye sclera is easily achievable. In this study, a visible red helium neon (632.8 nm HeNe) laser was chosen for the OMT tracking device.

Using International Electrotechnical Commission (IEC 60825-1)²⁷ and American National Standards Institution (ANSI Z136.1),²⁸^,²⁹ limits for the safe exposure of eyes and skin to laser radiation the MPE values for a direct intrabeam viewing of a 632.8-nm wavelength laser for 10s exposure time to an eye with a 7-mm pupil diameter was found to be 388.65 μW. It should be noted that this value is for an exposure to the retina, however, in normal use we are aiming the laser at the sclera and hence there is less risk of retinal eye damage.

To summarize, the following design parameters were calculated for our system: (1) a lens focal length of 150 mm; (2) a beam radius of 0.6 mm; (3) an aperture size of 25 mm; (4) a laser wavelength of 632.8 nm; and (5) a laser power of 136 μW.

2. Methods

In the following experiments, we aim to demonstrate the feasibility of using the speckle correlation method for measuring the rotation of objects with OMT-like movements. The proposed measurement system must be tested at eye-safe laser levels for its ability to meet OMT measurement specifications in terms of accuracy, resolution, range, and robustness to larger eye movements. To perform these tests both an OMT simulator and a manually adjusted gimbal were used to simulate the moving eye. A piece of cardboard was inserted into the gimbal to act as the target material and, similarly, another piece of the same cardboard was attached to the plastic of the simulator.

The optical setup for the experiment is shown in Fig. 2, the EMCCD sensor is placed in the fourier plane of the lens, i.e., at $z_{2} = f$ . The target is illuminated by a 632.8 nm plane polarized HeNe laser, which is reduced down to an eye-safe power of 139 μW by the use of a neutral density filter and a beamsplitter. The speckle pattern generated on the target is collected by an EMCCD camera (Cascade $128 +$ , Roper Scientific³⁰) operating at 500 Hz with a $128 \times 128$ array of 24 μm pixels, and a 100% fill factor. A 5 second (2500 frames) reading is taken for each measurement. The 8-bit digitized speckle images are then sent to the numerical software package Matlab³¹ for processing. The analysis procedure is shown in Fig. 3.

Fig. 2

Experimental setup.

Fig. 3

Analysis procedure.

During the processing each displaced speckle-image frame is cross-correlated with the original reference speckle-image frame. The full $128 \times 128$ pixels are used for every image during the cross-correlation analysis. To increase the accuracy in finding the exact correlation peak, and consequently the speckle displacement, the location of the cross-correlation peak is calculated with a subpixel algorithm. The subpixel correlation method used in this experiment is based on the curve-fitting method as described by Hung et al.³² The change in correlation peak location over time is used to calculate the pixel displacement of the speckle images.

Using Eq. (1), the calculated pixel displacement, $p_{x}$ , is converted to the measured angular displacement, $θ$ . To remove noise outside the desired frequencies, the signal is then filtered using a digital Butterworth filter of order five with a bandwidth of 20 to 150 Hz. A peak detection algorithm is used to measure each peak and trough in the recovered signal. To find the amplitude of the signal, each trough is subtracted from each peak, and the mean value is taken to be the peak-to-peak amplitude of the measured signal. To calculate the frequency content of the signal, a periodogram is utilised to estimate the power spectral density.

2.1.

Simulator Tests

An OMT simulator was used to test the measurement resolution, amplitude response, and frequency response of the system. The simulator replicates OMT movement in terms of typical frequencies and amplitudes. It was first designed by Sheahan¹⁶ but has since been revised and updated. A picture of the simulator is shown in Fig. 4. The two outer piezoelectric bimorphs of the simulator displace in response to an applied voltage, and the inner bimorph is used as a reference for calibration. The bimorphs are attached to a piece of plastic on one end. As the bimorphs bend the attached plastic tilts at an angle that is proportional to the applied voltage.

Fig. 4

OMT simulator. The small prism attached to the plastic disc is used during calibration of the simulator.

2.1.1.

Amplitude response at OMT rotation angles

The amplitude response of the proposed setup was tested first with varying frequency and then at various input amplitudes.

To test the amplitude response with varying input amplitude, the simulator was driven at the typical mean OMT frequency of 80 Hz and at OMT like amplitudes ranging from 4 to 197 μrad peak-peak in steps of 20 μrad. The experiment was repeated five times.

The lowest measurable amplitude that was recovered is given as the resolution of the system.

2.1.2.

Frequency response

To test the frequency response, a signal generator was used to drive the simulator sinusoidally with frequencies in the OMT range ranging from 10 to 150 Hz in steps of 10 Hz at an amplitude of 197 μrad peak-to-peak. 197 μrad was chosen since it was the maximum amplitude achievable with the frequency generator.

2.1.3.

Robustness to setup

Next an investigation of the impact of the $z$ -axis (the optical axis) location of the target on the accuracy of the system was performed. Using a linear translation stage, the distance between the simulator and the lens was altered in steps of 1 mm up to a maximum allowable translation of 50 mm. An angular displacement of 197 μrad and frequency of 80 Hz was applied and measured at each step before the simulator was displaced again.

2.1.4.

Toleration to linear displacement during measurement

To investigate the toleration of the system to a linear $a$ -axis displacement during measurement, the translation stage was used to create a 3 mm displacement along the axis while the simulator was running. Experimentally, 3 mm was found to be the most repeatable distance at which the translation stage could be displaced by hand during the 5 s recording time. The experiment was performed at a typical OMT amplitude of 87 μrad. An 80 Hz sinewave signal was used to drive the simulator over a period of 5 s while the simulator was moved along the translation stage by hand. Each translated speckle image was correlated with the original undisplaced reference frame.

Next, the toleration of the system to an $x$ -axis displacement was investigated. In this case a linear displacement of 50 μm was applied by hand using the translation stage. The simulator was again set to run at 80 Hz and 97 urad peak-to-peak. 50 μm (4.3 mrad) was chosen since it is within the expected measurable displacement of the system (10 mrad).

2.2.

Gimbal Tests

A gimbal (Melles Griot, 07MAD701) was implemented to test the amplitude response of the system over a range of angles larger than those achievable with the simulator. The gimbal, shown in Fig. 5, has an azimuthal resolution of 50 μrad and was used to rotate the target around the $y$ -axis.

Fig. 5

Gimbal configuration.

2.2.1.

Large angle amplitude response

To test the amplitude response of the system at larger angular displacements within the dynamic range of the system, the gimbal was rotated at the following frame-to-frame angular displacements 0.2, 0.25, 0.5, 0.75, 1, 2, 3, 4, 5, 6, 7, 8, 9, and 10 mrad. For each angle, the recorded speckle image was cross-correlated with its respective undisplaced reference image and the results were plotted.

3. Results

3.1.

Speckle Size

Figure 6 shows a typical cross-correlation peak resulting from the auto-correlation of a generated speckle pattern. Assuming fully developed speckle and using Eq. (6), the size of the speckle calculated from the full width at half max of the correlation peak was found to be 33.63 μm. This is in close agreement with the theoretical value of 33.57 μm for a beam radius of 0.6 mm and lens of 100 mm focal length.²⁵

Eq. (2)

FWHM = 4 \sqrt{\ln 2} \sqrt{F} ρ_{0}

Fig. 6

Cross-correlation of speckle pattern.

3.2.

Simulator Results

3.2.1.

Amplitude response at OMT rotation angles

Figure 7 shows the results of the amplitude response tests using the simulator. As shown in the figure, the measured angular displacements agree well with the applied angular displacement. The mean percentage error was found to be 12%. At a typical OMT amplitude of 87 μrad the percentage error was less than 10%, below 50 μrad the error increased above 10% to a maximum of 33% at 4 μrad.

Fig. 7

Input versus output displacement for the simulator at 80 Hz. The error bars show the standard deviation of the measurements.

The results show that the measurement system is capable of measuring angular displacements in the OMT range of 12 to 200 μrad. Further, the system resolution was determined to be at least 4 μrad. This is in agreement with the resolution requirements derived in Sec. 1.3.