the answer. neuro-imaging, such as mri scan, would be useful for confirmation of clinical findings. cognitive influences the pupillary response to light is not purely reflexive, but is modulated by cognitive factors, such as attention, awareness, and the way visual input is interpreted. for example, if a bright stimulus is presented to one eye, and a dark stimulus to the other eye, perception alternates between the two eyes (i.e., binocular rivalry): sometimes the dark stimulus is perceived, sometimes the bright stimulus, but never both at the same time. using this technique, it has been shown the pupil is smaller when a bright stimulus dominates awareness, relative to when a dark stimulus dominates awareness. this shows that the pupillary light reflex is modulated by visual awareness. similarly, it has been shown that the pupil constricts when you covertly (i.e., without looking at) pay attention to a bright stimulus, compared to a dark stimulus, even when visual input is identical. moreover, the magnitude of the pupillary light reflex following a distracting probe is strongly correlated with the extent to which the probe captures visual attention and interferes with task performance. this shows that the pupillary light reflex is modulated by visual attention and trial-by-trial variation in visual attention. finally, a picture that is subjectively perceived as bright (e.g. a picture of the sun), elicits a stronger pupillary constriction than an image that is perceived as less bright (e.g. a picture of an indoor scene), even when the objective brightness of both images is equal. this shows that the pupillary light reflex is modulated by subjective (as opposed to objective) brightness. mathematical model pupillary light reflex is modeled as a physiologically-based non-linear delay differential equation that describes the changes in the pupil diameter as a function of the environment lighting: m ( d ) = tanh − 1 ⁡ ( d − 4.9 3 ) d m d d d d d t + 2.3026 tanh − 1 ⁡ ( d − 4.9 3 ) = 5.2 − 0.45 ln ⁡ ( φ [ t − τ ] 4.8118 × 10 − 10 ) m(d)&=\tanh ^\left(\right)\\ m} d}} d} t}}+2.3026\tanh ^\left(\right)&=5.2-0.45\ln \left(\right)\end where d is the pupil diameter measured in millimeters and φ ( t − τ ) is the luminous intensity reaching the retina in a time t , which can be described as φ = i a : luminance reaching the eye in lumens/mm2 times the pupil area in mm2. τ is the pupillary latency, a time delay between the instant in which the light pulse reaches the retina and the beginning of iridal reaction due nerve transmission, neuro-muscular excitation and activation delays. d m m} , d d d} and d t t} are the derivatives for the m function, pupil diameter d and time t . since the pupil constriction velocity is approximately 3 times faster than (re)dilation velocity, different step sizes in the numerical solver simulation must be used: d t c = t c − t p s d t d = t c − t p 3 s \mathrm t_&=-t_\\\mathrm t_&=-t_\end where d t c t_ and d t d t_ are respectively the d t t} for constriction and dilation measured in milliseconds, t c and t p are respectively the current and previous simulation times (times since the simulation started) measured in milliseconds, s is a constant that affects the constriction/dilation velocity and varies among individuals. the higher the s value, the smaller the time step used in the simulation and, consequently, the smaller the pupil constriction/dilation velocity. in order to improve the realism of the resulting simulations, the hippus effect can be approximated by adding small random variations to the environment light (in the range 0.05–0.3 hz).