2.1.

Subjects

Right eyes from 18 Caucasian subjects, nine females and nine males, aged from $20\text{to}57\text{years}$ were measured in this study. The mean age of all subjects was $32\pm 10\text{years}$ . None of the subjects were using ocular or systemic medications and none were contact lens wearers. No subject reported any history of significant ocular pathology, injury, or surgery. The study was approved by the university research ethics committee, and all subjects gave informed consent before participation and were treated in accordance with the Declaration of Helsinki.

All subjects were clinically assessed as having a tear film quality within normal limits with no evidence of ocular pathology. The clinical assessment included clinical history, slit lamp examination, phenol red thread test of tear volume, and fluorescein tear film break-up time (FTBUT). The slit lamp assessment included examination of the lid margins and meibomian glands, the bulbar and tarsal conjunctiva, and staining of the ocular surface with fluorescein and lissamine green dye. The central lower tear meniscus height was measured with a slit lamp graticule. All subjects recorded a phenol red thread wetted length of greater than $10\mathrm{mm}$ . Three measurements of FTBUT were conducted and the average was taken. Fluorescein staining of the cornea and lissamine green staining of the bulbar conjunctiva were graded according to the National Eye Institute (NEI) grading scale.²² All subjects exhibited corneal and conjunctival staining scores of less than 3. The group average statistics of the clinical measurements, including the mean, standard deviation, median, and the median average distance (MAD), are shown in Table 1 .

Table 1

Group average statistics of the objective clinical measurements.

2.2.

Measurement Protocol

For each of the subjects, all measurements were taken in the afternoon within a two-hour time frame between 3 and 5 pm. To ensure that the room environmental conditions did not significantly affect tear film quality, all three instruments were located in the same room (see Fig. 1 ). Temperature and humidity of the room were controlled and recorded at the beginning of each measurement session. The average $(\text{mean}\pm \mathrm{SD})$ temperature in the measurement room was $(23\pm 1°\mathrm{C})$ and the average humidity was $(53\pm 5\mathrm{\%})$ .

Fig. 1

Measurement setup (a collage). From left: lateral-shearing interferometer (LSI), dynamic wavefront sensor (DWS), and high-speed videokeratoscope (HSV). Insets show examples of video frames from each of the instruments. Measurements were conducted in the following sequence: $\mathrm{HSV}\Rightarrow \mathrm{DWS}\Rightarrow \mathrm{LSI}$ .

Due to the need to save large amounts of digital data, the order of use of the instruments was standardized to optimize time management and reduce subject fatigue. Two measurements were taken with each instrument in the following order: high-speed videokeratoscopy (HSV), followed by dynamic wavefront sensing (DWS), and finally lateral shearing interferometry (LSI). During the measurements, subjects were asked to focus on the instrument’s fixation target and blink as naturally as possible without deliberately keeping their eyes open during a $30\text{-}\sec$ measurement period. A break of about $60\sec$ was allowed for the subject before a further $30\text{-}\sec$ measurement was taken. Data were excluded from analysis if there was obvious reflex tearing and significant eye movements during measurements (i.e., subject not focusing on the target). These decisions were made by an experimenter who was masked to the clinical tear analysis results. Five subjects out of the initially enrolled 23 subjects were excluded from further analysis.

2.3.

Instrumentation

For completeness, a short summary of the technical aspects of each of the three procedures is given. However, greater detail of each of the procedures can be found in the work of Alons-Caneiro, Iskander, and Collins for HSV,¹⁹ in the works of Iskander and Zhu for the DWS technique,^{20, 21} and in the works of Szczesna and Szczesna and Iskander for LSI.^{14, 23}

The HSV and LSI techniques captured images at a constant rate of $25\mathrm{Hz}$ , while the DWS provided sampling frequencies that fluctuated around $7.5\mathrm{Hz}$ . For each of the methods, blinks were automatically detected in the image sequences, and each sequence was divided into a series of interblink intervals.

During recordings, the eye undergoes natural micromovements,²⁴ which represent an interference that needs to be detected, because it can cause motion-related blur of the images. This effect is particularly evident in the HSV and LSI measurements. Hence, algorithms were developed to detect the images affected by the blur motion. Such blurred images were subsequently excluded from the analysis in both methods.

2.3.1.

High-speed videokeratoscopy

The image processing technique from HSV recording operates on the set of images within the interblink interval and involves the following steps.¹⁹ First, estimation of the region of interest is performed. Once the region with the fundamental information is extracted, the next step is to detect the unaltered ring pattern within this area. The technique separates the parts of the image that present a well-structured Placido disk pattern from the interference. After this, the interference is further clustered into two types, depending on the cause. Once the interference from eyelashes has been removed, the remaining interference is assumed to be related to the poor quality tear film.

Finally, tear film surface quality is estimated in the area of analysis (AOA), formed by the area related to the unaltered videokeratoscopy pattern signal and tear disturbance interference. The tear film surface quality indicator is estimated by using the method of image coherence analysis, in which the value of this indicator for each image is the average of the coherence measurement across the area of analysis.¹⁹ Examples of tear film surface quality kinetics estimated within the area of analysis ${\mathrm{TFSQ}}_{\mathrm{AOA}}$ , and within the pupil area, ${\mathrm{TFSQ}}_{\text{pupil}}$ , are shown in Fig. 2 . The pupil area was used for comparison with the DWS and the LSI techniques that are limited to measuring this region of the ocular surface.

Fig. 2

Examples of the tear film surface quality (TFSQ) dynamics recorded with HSV within the area of analysis (top) of approximately $78{\left(\mathrm{mm}\right)}^2$ and within the pupil area (bottom) of approximately $38{\left(\mathrm{mm}\right)}^2$ , in which the tear film build-up phase is clearly visible. Gaps in the records indicate the location of blinks that were removed from the dataset.

2.3.2.

Dynamic wavefront sensing

The Complete Ophthalmic Analysis System (COAS^™, WaveFront Sciences, Incorporated) was used for dynamic wavefront sensing. Measurements were performed in a multifile mode. Sampling instabilities are taken into account in the analysis by registering the exact time stamp of each single measurement. Since natural blinking occurred during data acquisition, a procedure for detecting the blinks in the original Hartmann-Shack images was used.

The remaining Hartman-Shack images were used to estimate the wavefront aberrations that were decomposed into Zernike terms, up to and including the eighth radial order, resulting in 45 time-varying coefficients. For this, the instrument’s own modal Zernike polynomial fitting algorithm was used. Finally, time series of total, higher-order, comatic terms, and the Zernike polynomial rms fit error were used as possible indicators of tear film surface quality.^{10, 11, 12, 18, 25}

Wavefront aberrations are also affected by the variations in pupil size, and since the time-varying Zernike polynomial coefficients are calculated for a given pupil size, it is necessary to rescale such coefficient values to a common pupil size.²⁶ Wavefront aberrations were rescaled to the smallest common pupil diameter in each of the recordings. Examples of wavefront dynamics are shown in Fig. 3 , where the time series of total aberrations (TAs), higher-order aberrations (HOA), total comatic terms ( ${\text{Coma}}_{\mathrm{V}}$ , and ${\text{Coma}}_{\mathrm{H}}$ , and the Zernike polynomial rms fit error are given. The total comatic terms include the third, fifth, and seventh order comatic terms.

Fig. 3

Examples of the wavefront aberration dynamics (values are in microns). From top to bottom: total wavefront aberrations (excluding piston and prisms), higher-order aberrations, total vertical coma, total horizontal coma, and the Zernike polynomial rms fit error. Gaps in the records indicate the location of blinks that were removed from the dataset.

Wavefront dynamics are affected by signals of the cardiopulmonary system, such as pulse and respiration.^{20, 21} In particular, this effect is prominent in the lower-order aberrations of defocus and astigmatism.²⁷ However, changes in comatic terms (both horizontal and vertical) have been shown to be associated with tear film kinetics.¹⁸

2.3.3.

Lateral shearing interferometer

In the LSI apparatus,^{14, 28} the wavefront generated from the HeNe laser illuminates the tear film on the cornea and reflects from its surface. The reflected wavefront is split in the LSI optical wedge into two wavefronts that interfere with each other to create an interferogram. For an evenly spread precorneal tear film, the fringes are regular and horizontal. In the case of an uneven tear film surface, the interference fringes reveal irregularities, and their background is inhomogeneous.²⁹ The central part of the cornea is exposed to the laser light, thus the tear film in the pupil area (approximately $4\times 4\text{-}\mathrm{mm}$ square region) is measured.

Assessing tear film surface quality from interferometric images is based on estimates of the first harmonic of the interference fringes.¹⁴ The technique combines the traditional spectral estimation techniques with morphological image processing techniques,²³ in which a smoothed 2-D periodogram [fast Fourier transform (FFT)-based spectral estimator] is treated like an image, from which local maxima are extracted and classified according to a set of criteria. Finally, a spatial-average localized-weighted estimate of the first harmonic is used as a measure, called M2, of tear film surface quality. An example of the tear film surface quality recorded with the LSI is shown in Fig. 4 . The data show the kinetics of the tear film surface after every blink recorded during the sequence. Immediately after each blink, the tear film stabilizes and reveals irregularities. The values of the TFSQ descriptor are high (worse quality) at the beginning, but decrease (better quality) with the tear film build-up time. It has previously been shown that the interferometric method is able to clearly observe the phenomenon of the tear film build-up immediately after each blink.²⁹

Fig. 4

An example of the tear film surface quality recorded with LSI. Gaps in the record indicate the location of blinks that were removed from the dataset.

2.4.

Blinking Patterns

Each of the three considered techniques for noninvasive measurement of tear film surface quality are based on different physical principles, have a different illumination source, and involve a different subject-instrument interface (i.e., headrest, proximity to instrument’s elements, fixation target). Hence, in the initial part of the study, it was important to determine whether the blinking patterns naturally exhibited by subjects changed from one instrument to another.

The group mean interblink interval $(\text{mean}\pm \mathrm{SD})$ across the instruments was $3.54\pm 2.52$ , $2.78\pm 2.48$ , and $3.18\pm 1.73\sec$ for HSV, DWS, and the LSI, respectively. Statistical testing by means of the repeated measures ANOVA revealed that across the individual subjects, there were statistically significant differences $(p<0.05)$ in the interblink interval. However, the type of instrument that was used did not cause statistically significant differences $(p>0.05)$ . Also, no statistically significant differences were identified when comparing the first $30\text{-}\sec$ measurement to the second measurement, indicating that the subjects’ blinking patterns were similar in the two consecutive measurements with each of the instruments. The lower sampling rate in DWS $\left(7.5\mathrm{Hz}\right)$ as compared to that of HSV and LSI $\left(25\mathrm{Hz}\right)$ had little effect on the estimated variability of blink patterns.

2.5.

Tear Film Parameter Estimation

The time series of a tear film surface quality indicator within an individual interblink interval is used to estimate two parameters: the tear film build-up time $T_{\mathrm{BLD}}$ , and the average tear film surface quality ${\mathrm{TFSQ}}_{\mathrm{Av}}$ , in the stable phase of the interblink interval. This phase is defined as a period from the end of the tear film build-up phase to the end of the interblink interval. Statistical modeling of tear film surface quality has been considered earlier in the context of interferometric data,³⁰ where a set of four parametric functions has been considered: a bilinear, a trilinear, Hoerl’s, and an optimal polynomial function.

The bilinear function seems to be appropriate for the analysis of tear film surface quality in interblink intervals for subjects with normal tears, as they usually exhibit up to two phases of the tear film kinetics (i.e., the tear film build-up phase and the relatively stable interblink phase). In this work, we have extended the bilinear function model so that the second linear function describing the stable interblink phase is constrained by the estimator of the first linear function describing the tear film build-up phase. This is performed using an iterative nonlinear constrained least-squares approach. An example of such bilinear fitting is shown in Fig. 5 .

Fig. 5

An example of the estimated tear film surface quality in an interblink interval with a constrained bilinear fit. The intercept of the two linear functions is the estimator of the tear film build-up time $T_{\mathrm{BLD}}$ . The estimator ${\mathrm{TFSQ}}_{\mathrm{Av}}$ corresponds to the average of TFSQ taken from the intercept to the end of the interblink interval.

Since the two distinct phases of tear film behavior cannot always be observed in all measured interblink intervals, it was necessary to test in each sequence whether a bilinear fit is warranted. This has been achieved by performing a log likelihood ratio test of the Pearson’s correlation coefficients for a linear and bilinear fit, as suggested by Owsley, Knoblauch, and Katholi.³¹ In summary, the estimated Pearson’s correlation coefficients $r_{\mathrm{Lin}}$ and $r_{\mathrm{BiLin}}$ are first transformed using Fisher transformation and are multiplied by a factor $\sqrt{N-3}$ , with $N$ being the number of sample points, to become standard normal $z_{\mathrm{Lin}}$ and $z_{\mathrm{BiLin}}$ . Then the log likelihood ratio $-2\log [f\left(z_{\mathrm{Lin}}\right)∕f\left(z_{\mathrm{BiLin}}\right)]$ , where $f\left(z\right)$ denotes the standard Gaussian probability density function, and is ${\chi }^2$ distributed with $2\mathrm{deg}$ of freedom. The $p$ -value for which the linear fit was rejected in this test was set to $p<0.01$ .

3.1.

Tear Film Build-Up Time

The group statistics of the tear film build-up time measures $T_{\mathrm{BLD}}$ , acquired from the three considered instruments, are shown in Table 2 . Since the data did not always follow a Gaussian distribution, we also considered the median and the median absolute deviation (MAD).

Table 2

Group statistics of the tear film build-up time across the instruments.

For the HSV, the group average $T_{\mathrm{BLD}}$ was $1.14\sec$ when calculated across the whole visible corneal surface (AOA) and was $0.99\sec$ in the pupil area, while the group median values were $0.60\text{to}0.66\sec$ , respectively. Five descriptors of $T_{\mathrm{BLD}}$ were used in the case of the DWS method. They were based on total aberrations (TA), higher-order aberrations (HOA), total vertical coma $\left({\text{Coma}}_{\mathrm{V}}\right)$ , total horizontal coma $\left({\text{Coma}}_{\mathrm{H}}\right)$ , and the Zernike polynomial rms fit error. An increased variability of tear film surface parameter estimates is apparent in the results from the DWS. The group average $T_{\mathrm{BLD}}$ ranged from $1.57\sec$ for vertical coma to $2.46\sec$ for horizontal coma. Median-based statistics did not reduce the variability, but rather shifted it toward shorter values (i.e., ranged from $0.75\text{to}1.92\sec$ ). The group average of the $T_{\mathrm{BLD}}$ measure acquired from LSI was $0.89\sec$ . It is worth noting that the estimated median values for HSV in the pupil area and for vertical coma in DWS are remarkably close to the estimates of median $T_{\mathrm{BLD}}$ from LSI.

To ascertain whether the two distinct phases of tear film behavior—the build-up phase and the stability phase—were observed in all measured interblink intervals, a count was kept on how many times the hypothesis of a single linear fit (rather than the bilinear fit) to the interblink data was rejected. The number of rejected linear fits to the data was on average 20, 42, and 98% of the total number of interblink intervals for the HSV, DWS, and the LSI, respectively (see the percentage count in Table 2). This indicates that the phase of tear film build-up was almost always observed with the LSI technique, but not using the HSV and DWS methods. No cases were encountered in which the hypothesis of the linear fit to the data was retained for all interblink intervals in the measurement.

3.2.

Tear Film Surface Quality

The statistics of the average tear film surface quality in the stable phase of the interblink interval ${\mathrm{TFSQ}}_{\mathrm{Av}}$ , acquired from HSV using the entire visible corneal area (AOA) and the pupil area, are shown in Table 3 . The estimated averages and standard deviations are very close to median and MAD values, indicating only small numbers of outliers. We note that the tear film quality within the pupil is, as expected, slightly better than across the whole area of analysis.

Table 3

Group statistics of TFSQAv acquired from HSV.

The statistics of the tear film parameters acquired from DWS are shown in Table 4 . Large variations were observed between the mean/standard deviation and median/MAD statistics only for ${\mathrm{TFSQ}}_{\mathrm{Av}}$ based on total aberrations.

Table 4

Group statistics of TFSQAv acquired from DWS.

The statistics of the tear film parameters acquired from LSI are shown in Table 5 . As in the case of the HSV technique, there was not much difference between the mean/standard deviation and median/MAD statistics.

Table 5

Group statistics of TFSQAv acquired from LSI.

The mean and median values for the estimator of ${\mathrm{TFSQ}}_{\mathrm{Av}}$ are similar, indicating that the data are not skewed and are free of outliers. This is not the case for the estimator of $T_{\mathrm{BLD}}$ , where median values were consistently lower than the mean values. One possible explanation is the observed nature of the build-up phase that occasionally exhibits longer periods of tear film formation, and hence does not follow a Gaussian distribution.

3.3.

Instrument Precision

To ascertain the precision of the instrument in measuring ${\mathrm{TFSQ}}_{\mathrm{Av}}$ , the coefficient of variation CV was also calculated. First, the coefficient of variation was calculated using the original TFSQ data in the stable phase of the interblink interval. This was followed by calculating the coefficient of variation for detrended data, in which the linear trend in TFSQ was removed. The group statistics of the coefficient of variation for the ${\mathrm{TFSQ}}_{\mathrm{Av}}$ are given in Table 6 .

Table 6

Group statistics of the coefficient of variation (CV) across the instruments.

The coefficient of variation for ${\mathrm{TFSQ}}_{\mathrm{Av}}$ in HSV was found to be very low (below 1%). The precision of the DWS in quantifying tear film surface quality was found to be more variable. The coefficient of variation for ${\mathrm{TFSQ}}_{\mathrm{Av}}$ ranged from about 1.5% for the total aberrations to about 15% for the horizontal coma, when the linear trend in the TFSQ was removed. This result was expected, as the total aberrations, which are dominated by the spherical and cylindrical components, are usually more stable than the higher-order aberrations. The coefficient of variation for ${\mathrm{TFSQ}}_{\mathrm{Av}}$ for the LSI method was also found to be low at 3%.

3.4.

Correlation between Instruments

Pearson’s $r^2$ coefficient was calculated to ascertain the correlation between $T_{\mathrm{BLD}}$ and ${\mathrm{TFSQ}}_{\mathrm{Av}}$ measured with each pair of the three considered instruments. The results are shown in Tables 7, 8 .

Table 7

Correlation between TBLD measured with the three instruments. The asterisk indicates statistically significant values (p<0.01) .

Table 8

Correlation between TFSQAv measured with the three instruments. The asterisk indicates statistically significant values (p<0.01) .

Moderate but significant correlation was found between $T_{\mathrm{BLD}}$ measured with LSI and DWS based on the vertical coma ( $r^2=0.34$ , $p<0.01$ ), and between LSI and DWS ( $r^2=0.31$ , $p<0.01$ ) based on the high-order aberrations. Also, moderate but significant correlation was found between ${\mathrm{TFSQ}}_{\mathrm{Av}}$ measured with LSI and HSV ( $r^2=0.35$ , $p<0.01$ ) and between LSI and DWS ( $r^2=0.40$ , $p<0.01$ ) based on the rms fit error. No significant correlation was found between HSV and DWS for both $T_{\mathrm{BLD}}$ and ${\mathrm{TFSQ}}_{\mathrm{Av}}$ .

Statistical significance testing by means of the repeated measures ANOVA for each of the instruments revealed that across the subjects, there are statistically significant differences $(p<0.05)$ in $T_{\mathrm{BLD}}$ and ${\mathrm{TFSQ}}_{\mathrm{Av}}$ , suggesting that the tear film build-up process as well as the tear film quality level are different between subjects. However, for each of the methods, no statistically significant differences were found in ${\mathrm{TFSQ}}_{\mathrm{Av}}$ for an individual subject, across the interblink intervals (within a $30\text{-}\sec$ measurement period), or between the two sequential $30\text{-}\sec$ measurement periods. Considering the $T_{\mathrm{BLD}}$ computed for pairwise comparison across instruments, no statistically significant differences were observed between the HSV and LSI $(p>0.05)$ , while DWS showed statistically significant differences when compared to the other two instruments. Hence, as expected from the descriptive statistics, HSV and LSI provide close agreement for measurements of $T_{\mathrm{BLD}}$ , while DWS differs from the HSV and LSI results.