Supplementary Information
Title: Microsaccades are different from saccades in scene perception
Journal: Experimental Brain Research
Authors: Konstantin Mergenthaler*, Ralf Engbert, University of Potsdam, Potsdam, Germany
*Email: Konstantin.Mergenthaler@uni-potsdam.de
To check the reliability of our microsaccade detection procedure, we apply two qualitatively different
statistical methods to exclude two possible sources of artifacts. The first method is based on a
statistical bootstrapping approach (Engbert & Mergenthaler, 2006). Here we applied a simplified
version of the Monte-Carlo technique. For each trial from the scene perception data, we determined all
saccades with amplitudes larger than 1° and divided the eye-movement data into saccades and
fixations. For each fixation, we computed the corresponding time series of eye velocities. These
velocity samples were randomly shuffled in order to destroy all correlations between subsequent data
samples (Theiler et al., 1992). To construct surrogate data for the eye trajectories, we then computed
the cumulative sum of velocity samples. It is important to note that the distribution of the velocity
samples in the surrogate data was exactly the same as in the original data. Finally, we applied the same
detection algorithm to both surrogate and original data. As a result, we obtained a clear difference in
the distributions of microsaccade amplitudes between original data and surrogates (Fig. S1). We
conclude that our detection algorithm reliably detects epochs of the eye’s trajectory with increased
autocorrelation. In an earlier analysis (Mergenthaler & Engbert, unpublished), we observed that
microsaccades generate the most important contribution to autocorrelation found in fixational eye
movements. From this perspective, the surrogate analysis discussed here supports the view that the
bimodality of the data in Fig. S1 is due to microsaccades.
The second method is based on the critical assumption that microsaccades are binocular events. While
the binocularity criterion is very reliable for large saccades it cannot supply a lower bound, without the
evaluation of false alarms. Decreasing values of the detection threshold inevitably produce an
increasing number of monocular events. If the monocular event are very frequent, then binocular
events will be found frequently by changes. Therefore, developed an algorithm which identifies how
many binocular events do occur by chance. The number of binocular events detected in original data
can than be corrected by the number of events explained by random coincidence. The algorithm
consists of several steps:
1. All (micro)saccades are identified as binocular events with a large threshold multiplier (6).
These (micro)saccades are removed from the eye movement trajectory as described in part
one, but are stored as reliably detected saccades.
2. Next, all monocular events are detected in right and left eyes for a smaller threshold multiplier
(Fig. S2 shows the results for values of =2, 2.5, 3, 3.5, 4, and 5).
3. For the two monocular streams of events the binocular ones are identified and considered
microsaccade candidates.
4. A surrogate stream of events is created. The same monocular events are used, but instead of
directly applying the binocularity criterion, the data from one eye is temporally inverted, e.g.,
an event between time points t1 to t2 in a trial of length N is inverted to the interval between
N–t2 and N–t1. Therefore, the surrogate event series maintains inter-event intervals and
durations, while destroying any correlations across eyes. Note: As this method is prone to
randomly combining real microsaccades (i.e., those detected at the larger threshold in step 1.)
it dictates to operate on the reduced data set without (micro)saccades detected at the larger
threshold.
5. The number of binocular events obtained in step 3. is now reduced by the number of random
coincidences in step 4.
6. Finally, the (micro)saccades identified in step 1. are added to the (micro)saccades.
Results are plotted in Fig. S2. First, the is an increasing number of microsaccade candidates for
decreasing values of the threshold. However, the number of random coincidences (from the
bootstrapping procedure) increases even faster than the number of microsaccade candidates. As a
results, the remaining number of microsaccade candidates (reduced by the number of random
coincidences) starts to fall for threshold values smaller than 3 Thus, the optimal detection
threshold, which verifies the bimodality of the distribution, can be found in a range between 3 and
3.5
References
Engbert R, Mergenthaler K (2006) Microsaccades are triggered by low retinal image slip. Proc Natl
Acad Sci USA 103: 7192–7197
Mergenthaler K, Engbert R Microsaccade detection: Statistical testing using surrogate data and effects
of inter-individual differences and variations in luminance. Unpublished manuscript
Theiler J, Eubank S, Longtin A, Galdrikian B, Farmer JD (1992) Testing for nonlinearity in timeseries—The method of surrogate data. Physica D 58: 77–94
Fig S1. (A,C,E) Comparison of amplitude distributions during scene viewing of original data and
surrogates generated within fixations. (A) Saccadic-events were detected with a threshold multiplier
=2.5. The pronounced maximum at 0.05° in the surrogate data suggests that the threshold multiplier
is too small is this case. (C) Saccadic-events were detected with a threshold multiplier =3. This is the
value applied throughout the article. The maximum at 0.05° nearly disappears in the surrogate data,
which suggests that =3 is an adequate choice for the analysis of our data. (E) Saccadic-events were
detected with a threshold multiplier =4. The value appear to be too large to observe the clear
bimodality in the amplitudes. (B,D,F) Comparison of inter-event intervals obtained for saccadic events
(<0.4°) for original data and surrogates.
Fig S2. Analysis of random coincidences of binocular events. The blue curve denotes the amplitude
histogram for the (micro)saccades detected for =6 (same curve for all plots). Across the figures from
A to F the threshold multiplier  for the additional reliable binocular microsaccades is varied in
increasing order (A: =2.0, B: =2.5, C: =3.0, D: =3.5, E: =4.0, F: =5.0). Rates of microsaccades
are given in the plots. The number of binocular events which could not be explained by random
concurrence increases from =2.0 to =3.0 and declines for higher Thus, the optimal signal-tonoise ratios is obtained in the range from =3.0 to =3.5.