Although valid TCA measurements could be derived from each individual frame at 30 Hz, registration data was recorded over a few seconds, in order to identify registration artifacts introduced by eye blinks and microsaccades (
). We found that image offsets between the color channels can be routinely measured with sub-pixel precision; the standard deviation of repeated measurements averaged 0.3 pixels. For the 1.2 deg field used, this error in the measurement corresponded to 2.55 arcsec of visual angle, or about one-tenth the diameter of the smallest cones in the fovea (1 arcsec equals ~80 nm of retinal space). Some of this measurement error can be attributed to a combination of small fixational drifts and ocular microtremor, with the latter causing within-frame image distortion due to its relatively high frequency [18
Fig. 6 Image offset measurement quality and significance. A) Frame-by-frame offsets calculated from a 5 s video. Colors code the red/infrared and green/infrared offsets, for x and y dimensions in the images. Arrows indicate artifacts introduced by microsaccades. (more ...)
Larger errors in the registration do occur when image quality degrades. This is an unwanted situation in which image stabilization and thus targeted light delivery is also unlikely to succeed. Measurement errors increased when imaging in the foveola where photoreceptors are harder to resolve, because image cross-correlations are compromised when contrast is reduced. However, enough image structure remains when imaging at the center of gaze such that TCA measurements can be made with single cone precision (see psychophysical validation below). Outside the foveola, TCA measurements reached sub-cone precision with high accuracy because the cone mosaic is well resolved. In 3 subjects, typical TCA offsets with a centered pupil position were about 5 pixels (42 arcsec), but could easily exceed 15 pixels (2 arcmin) during any one imaging session. Thus TCA offsets are normally greater than the distance between cone centers. Without correcting for these offsets, light delivery across color channels would necessarily stimulate different photoreceptors ().
To confirm the validity of the image-based TCA measurements, we compared these data to a subject’s ability to assess the positional offset of differently colored squares at the fovea. We made use of the exquisite sensitivity of the human visual system to detect offsets in the relative position of visual objects, a feat termed hyperacuity, because psychophysical thresholds in such tasks are lower than the sampling capacities of the cone photoreceptor lattice [19
]. Subjects were asked to center a 7 arcmin square (either red or green, tested separately) with respect to four equally sized and spaced stationary squares displayed in the infrared channel (
). To allow for the most accurate alignments, stimuli were presented foveally and the task was self-paced. In theory, subjective alignments between channels and our objective TCA measurements should be identical. For all three subjects, the differences between objective and subjective TCA measurements were small (). On average the difference was 0.95 pixels (8 arcsec). These differences are most likely due to residual system alignment offsets that exist between the light delivery and collection arms of the AOSLO; such system offsets are technically difficult to eliminate. The standard deviation of the objective measurement was consistent across subjects, and always lower than that of the psychophysical results (average SD in pixels, 1.03 objectively, 1.76 subjectively, equaling 8.8 and 15 arcsec, respectively). This demonstrates that the image-based TCA measurements presented here are functionally identical to that of conventional subjective TCA measurements [9
Fig. 7 Validation by hyperacute psychophysics. A) The psychophysical task required subjects to align a small colored square (red or green) within four flankers presented against the IR background (dark red). Each of 50 trials began with the colored square randomly (more ...)
The wide variation in TCA offsets present between subjects () is mostly due to misalignment of the instrument beam relative to the achromatic axis of each subject’s eye. In subject S1, for instance, the imaging beam appeared to be very close to the achromatic axis, because the TCA offsets were relatively small. One could eliminate these offsets by adjusting the pupil position using the method described below, if measurements were taken both vertically and horizontally. However, given the large pupil requirement for AO, it is possible that no pupil position adjustments could eliminate the resulting chromatic offsets, especially if the measurements are being done in the periphery. It is worth reiterating that this image-based method measures the combined offsets caused by dispersion as well as beam misalignment, and both need to be compensated.
Inferred from geometrical optics, the predominant factor contributing to TCA offsets in an LCA corrected imaging system are positional shifts of the pupil relative to the imaging beam (). We therefore used systematic pupil shifts to independently validate the image-based TCA measurements. To do this, we manipulated the beam position relative to the entrance pupil by moving the subject’s head horizontally in 0.25 mm steps and recorded the red and green channel TCA continuously (
). For each horizontal step we averaged the TCA values for 20 consecutive video frames. The results of these measurements agree with theoretical TCA values in the standard chromatic model eye [21
] (). Notably, lateral pupil displacements as small as 0.25 mm produce changes in TCA for the green channel that are about twice as large as the smallest cones in the fovea. These results emphasize how small pupil displacements, as they occur during gaze shifts or head movements, are a major cause of sizable dynamic changes in TCA offsets (
, Media 2
). As a practical note, as long as the bite bar position and fixation point were not changed, TCA measurements with practiced subjects going in and out of position did not shift by more than 1 or 2 pixels (measured over a time span of 1-1.5 hours).
Fig. 8 Validation by geometrical optics. A) Frame-by-frame TCA measurement while the pupil was shifted horizontally in 0.25 mm steps relative to beam center. B) The mean horizontal offset per step (dots) is plotted over theoretical calculation of TCA (lines) (more ...)
Fig. 9 TCA changes due to gaze shifts. Left: The subject’s pupil during image-based TCA measurements. The subject performs voluntary gaze shifts while fixating the four corners of the imaging field, corresponding to 1.2 deg of visual angle between each (more ...)