Prediction accuracy of L- and M-cone based human pupil light models

Abstract

Multi-channel LED luminaires offer a powerful tool to vary retinal receptor signals while keeping visual parameters such as color or brightness perception constant. This technology could provide new fields of application in indoor lighting since the spectrum can be enhanced individually to the users' favor or task. One possible application would be to optimize a light spectrum by using the pupil diameter as a parameter to increase the visual acuity. A spectral-and time-dependent pupil model is the key requirement for this aim. We benchmarked in our work selected Land M-cone based pupil models to find the estimation error in predicting the pupil diameter for chromatic and polychromatic spectra at 100 cd/m 2. We report an increased estimation error up to 1.21 mm for 450 nm at 60-300 s exposure time. At short exposure times, the pupil diameter was approximately independent of the used spectrum, allowing to use the luminance for a pupil model. Polychromatic spectra along the Planckian locus showed at 60-300 s exposure time, a prediction error within a tolerance range of ± 0.5 mm. The time dependency seems to be more essential than the spectral dependency when using polychromatic spectra. The pupil aperture is an essential factor in photometric and visual investigations because of its direct influence on both retinal illumination and the retinal image quality 1. A smaller pupil diameter can ensure a larger depth of field 2 and achieve a decrease of optical aberrations 3,4 , which has positive effects on the visual acuity of the eye 4,5. Visual acuity is relevant in the interior lighting of workplaces or production facilities since an enhanced visual performance leads to fewer accidents or human injuries 6. Various studies have shown that the optimal pupil diameter is approximately between two and three millimeters for visual tasks in the photopic luminance range 1,4,7-11. With today's technology of multi-channel LED luminaires, it is possible to optimize artificial light spectra to influence the pupil aperture, color perception, brightness perception or other lighting metrics 12,13. The number of narrow-band light-emitting diodes in such a system determines the degree of freedom, which allows keeping specific parameters constant while changing others. The first step to actively optimize the pupil aperture through illumination without influencing other image-forming vision parameters such as brightness or color perception is the construction of an accurate model which predicts the spectral and time-dependent pupil diameter. Such a model can be used in a heuristic or gradient-based optimization procedure as an objective or constraint function to design the desired light spectrum for visual tasks. Eight empirical models are proposed in the literature with different dependent parameters and test conditions. The most famous models are from Holladay 14 , Crawford 15 , Moon and Spencer 16 , De Groot and Gebhard 17 , Stanley and Davies 18 , Barten 19 and Blackie and Howland 20. In 2012, Watson and Yellot 21 reviewed these pup...

Deep learning-based pupil model predicts time and spectral dependent light responses

“…At one second exposure time, it was 0.71 ± SD 0.15 mm 25 . Furthermore, with chromatic spectra of the peak-wavelengths 450 nm, 530 nm, 610 nm and 660 nm, the averaged prediction error at one second adaptation time was 0.94 ± SD 0.12 mm 25 .…”

“…Therefore, the more rigorous application must make a significant contribution to the prediction accuracy, justifying the extra work. In a recent study, it was found that at 60 s exposure time, the mean prediction error of the Watson and Yellot pupil model with polychromatic white light of different correlated colour temperatures ( 2000 K, 5000 K, 10,000 K) is less than 0.5 mm 25 . At one second exposure time, it was 0.71 ± SD 0.15 mm 25 .…”

“…In a recent study, it was found that at 60 s exposure time, the mean prediction error of the Watson and Yellot pupil model with polychromatic white light of different correlated colour temperatures ( 2000 K, 5000 K, 10,000 K) is less than 0.5 mm 25 . At one second exposure time, it was 0.71 ± SD 0.15 mm 25 . Furthermore, with chromatic spectra of the peak-wavelengths 450 nm, 530 nm, 610 nm and 660 nm, the averaged prediction error at one second adaptation time was 0.94 ± SD 0.12 mm 25 .…”

“…Up to the equilibrium state of the pupil, the weighting proportion of the classical outer retinal photoreceptors and the ipRGCs is time dependent 38 . The period at which the equilibrium state is reached depends significantly on the retinal irradiance and the spectral power distribution of the stimulus 7 , 25 , 39 , 40 . Pupil examinations showed that the equilibrium state is reached faster with short-wavelength stimuli than with longer-wavelengths 25 , 39 , 41 .…”

“…is not sufficient. The temporal influence is much more significant than the spectral impact when using white polychromatic light spectra 25 .…”