Rather than shell out almost £3k for the Swarovski binoculars to test the forehead rest, I opted to make such a rest, customised to the shape of my forehead, for my Zeiss 10x42 T*FL binoculars.
Pointing stability was then measured by strapping a Motorola G7 Power Android smartphone to the optics and using the SensorData application to read out the 3-axis rate gyro data from the embedded Bosch BMI160 MEMS Inertial Measurement Unit. The data was sampled at 200 Hz and exported to the LibreOffice Calc spreadsheet for analysis. Measurements were taken with and without the forehead rest in position. Two stances were adopted: holding the binoculars with the elbows supported on a table while sitting, as might be done in a hide; and also while standing without other support. These four measurement sets were taken in rapid succession to ensure a uniform level of observer capability. Each measurement lasted for about a minute, and had large startup and shutdown transients associated with picking up and setting down the binoculars. These transients were removed from the dataset before further processing.
The output of the smartphone app consists of angular rates of change with time, but the angle time series was needed to assess hand shake amplitude. This was derived by cumulative summing of the rates of change. The output angle time series showed the expected fluctuations due to hand shake, superimposed on an apparently linear gyro drift. This drift was fairly consistent between measurements, but differed significantly among the three axes, and was never more than 1 mr/s. A linear regression analysis allowed removal of the gyro drift, and the hand shake amplitude appeared as the standard error in the regressive fit. These standard errors were found for each of the three orthogonal axes for the four cases described above. These are tabulated below (1mr = ‘1 in 1000’ = 3.4 minutes of arc) with roll, pitch and yaw axes defined as usual.
Hand shake magnitude (milliradians)
Stance | Roll | Pitch | Yaw |
Sitting with rest | 0.46 | 0.54 | 0.42 |
Standing with rest | 1.83 | 1.62 | 1.67 |
Sitting without rest | 0.45 | 1.02 | 0.66 |
Standing without rest | 1.40 | 1.44 | 2.34 |
It must be emphasised that is a moot point what can be read into these figures. The gyro drift might not be linear; even more to the point, holding binoculars still is mildly stressful, and performance degrades as tiredness sets in. The results were obtained by standard simple error analysis, with an assumption of a Gaussian error distribution, which may not be a good model, and the ‘error in the error’ cannot easily be found. Some appreciation of the latter could be obtained by multiple repeats of the measurement process, for which I lack the patience.
Comparing standing with sitting (elbows supported), it is evident, and unsurprising, that the pointing accuracy is improved in all axes by sitting. This improvement is about 3 - 4 times, with or without the forehead rest, except in yaw where it is a little less when standing. Comparing the performance with and without the forehead rest, it is seen that when sitting there is a substantial improvement of almost a factor of two in pitch with the rest in position. This might well be expected; however the improvement by about a factor of 1.5 in yaw is more surprising. When standing, the presence of the rest appears to mildly degrade performance in roll and pitch, but improve in yaw: as remarked above, caution should be applied to small changes.
In a separate analysis of the raw angular rate data using MATLAB, the gyro performance was checked by observing the noise floor spectrum while stationary and while rotated at 33.33 rpm. Its level was consistent with the specification of the device. The spectrum of the fluctuation rate revealed that most of the hand shake took place at low frequencies, below 15 Hz, as would be expected; more surprising (to the writer) there were clear spikes at 6.5, 9.8 and 10.9 Hz, which arise from natural hand tremor. This tremor was not apparent to the writer.
In summary, for this user:
Pointing accuracy was roughly 1 milliradian
About 3 times improvement in pointing accuracy resulted from sitting with elbows supported rather than standing
Use of the forehead rest improved pointing accuracy in pitch by almost twice when sitting; this leads to all three axes having similar hand shake, a worthwhile improvement
When standing it is questionable whether there is any benefit in using the forehead rest
