# Mouse vision

The mouse's eye was simulated using ISET, from the scene to the cone absorption outputs. The optics, sensor and pixel corresponding to the mouse eye are similar to the human's, but with different parameters. The code is a part of ISET : you can download it from the ISET svn repository, and look at the functions mentioned below.

#  Optics

##  Focal length (in opticsCreate.m)

Optics model of equivalent lens for the mouse (from Remtulla and Hallet, 1985)

In order to simulate mouse optics using ISET, we need to obtain several physical and geometric parameters, taken from an equivalent model of mouse eye optics.

The lens and cornea both participate in the shaping of the image. In the equivalent model (see figure), their effects are inserted in a single paraxial lens, with non-negligible thickness (for explanations on the different notations of the figure, you can see http://en.wikipedia.org/wiki/Cardinal_point_%28optics%29).

Such a lens has two focal lengths : the front focal length, before the optic system, measured by the distance between the front focal plane F and the front principal plane P, and the back focal length, after the optic system, measured between the back principal plane P' and the back focal plane F' and corresponding roughly to the lens-retina distance.

It is important to note that the refraction index of the medium in which the light propagates is different in the two cases : air before the optics (index of 1.003) and vitreous humor after the lens (index of about 1.33). In geometric optics, the distances are divided by the medium index, therefore using the back focal length would require the insertion of refraction indices in the ISET simulation.

Finally, the focal length value used for the simulation is the back focal length divided by the refraction index of vitreous humour, 1.756 mm. (This is also the value of the front focal length with air index of 1.)

##  Pupil size (in opticsCreate.m)

Mouse pupil: contracted, intermediate, dilated (from Pugh, 2004)

The pupil size is a necessary parameter for ISET's diffraction-limited OTF. Its measurement on the mouse is a delicate matter. We obtained values (Pugh, 2004) for the most contracted (0.178mm) and most dilated (1.01mm) pupil sizes (see image).

The value we used in ISET is the mean of the contracted and dilated pupil sizes, 0.59 mm. In reality, the pupil size will depend on illumination in a way that is unknown to us.

##  Defocus (in mouseCore.m)

Defocus of the mouse and human eye, as a function of wavelength, in diopters (data from Remtulla and Hallett, 1985)

The focal length measured earlier is in reality wavelength-dependent, we have to take chromatic aberration into account.

Different wavelengths will not focus exactly on the retina but at different distances from it: this is measured by the defocus (in diopters). We obtained (Remtulla and Hallett, 1985) defocus values for four wavelength for the mouse optics, which we interpolated linearly to the whole spectrum (see figure).

The human defocus is much lighter than the mouse's. It is interesting to note that the shape of the curve is not linear. The values for the mouse get really extreme in the short wavelengths (the UV color must be very blurred), but we would need more measures to confirm the interpolation. The focal length's main value (see above) corresponds to the wavelength of least defocus (544nm).

##  Optical transfer function (in mouseOTF.m)

Mouse optical transfer function (axes are wavelength and spatial frequency in cyc/deg)

Using ISET's diffraction-limited optics and the different mouse parameters, we obtain a simulation of the Optical Transfer Function.

The OTF depends on wavelength (axis to the front of the figure, from right to left), like the defocus. Around the in-focus wavelength (544nm), we see that the cutoff is less severe than at other wavelengths, because the image is less blurry. At the short wavelengths, the cutoff frequency is much smaller (around 1 cycle/degree).

As a comparison, the human eye can see until almost 30 cycles per degree.

##  Transmittance of the lens (in opticsCreate.m)

Transmittance of the mouse optics (from Jacobs 2003)

The lens transmits only a portion of the incident photons, in a way that depend on wavelength (see figure). The long wavelengths are allowed to pass almost entirely, whereas the short wavelengths are cut off, to protect the eye from UV radiation.

The mouse lens transmits well into the UV spctrum, with a transmittance of 38% at 325nm. In comparison, the human lens' cutoff point is at much longer wavelengths, with a transmittance of less than 0.5% at 425nm (data from Optical density of the human lens, Jun Xu, Joel Pokorny, and Vivianne C. Smith, Vol. 14, No. 5 / May 1997 / J. Opt. Soc. Am. A).

In real eyes, we should also consider the transmittance of the cornea, which we haven't done for this simulation. As an indication, the human corneal transmittance is almost linear with wavelength, with a value of about 50% at 400nm at 85% at 700nm (data from Portable light transmission measuring system for preserved corneas, Liliane Ventura1, Gabriel Torres de Jesus, Gunter Camilo Dablas de Oliveira and Sidney JF Sousa, BioMedical Engineering OnLine 2005, 4:70doi:10.1186/1475-925X-4-70).

#  Sensor (in sensorCreateConeMosaic.m)

We modeled the cones and the retina as an ISET sensor, a array of "pixels" with specific parameters. The mouse retina has a large number of small rods, interspaced with fewer cones. We didn't find clear information about the luminance levels required for rod and cone vision in the mouse, and experiments testing different aspects of mouse vision didn't specify the type of vision used either. Pugh (see references) has measured the bleaching of rhodopsin in mouse rods, but the light units are in human scotopic candelas /m2, which makes little sens for mouse vision. We decided to restrict the scope of the project to cones only, because the mouse's cones have surprising properties compared to the human's, that we wanted to investigate.

The mouse has only two types of photopigments (see figure). One has its absorption peak around 510 nm, similarly to the human M cone, and the other peaks in the UV, around 360 nm. A significant part of absorptions can therefore be in the UV range.

The cones of the mouse can express one of the two pigments, or both (for comparison, the human cones only express one type of pigment per cone.). Mouse cones are refered to as M, UV and mixed, and the relative quantity of each pigment in mixed cones can vary. There is no precise consensus yet about the repartition of the cones and pigments in the retina, as different measurement methods have given slightly different results, but the community generally agrees that the cones are not organized in a mosaic of intermixed cones (like in the human retina, or camera sensors) but rather separated in different regions of the retina. There is mostly M pigment/cones in the dorsal part and mostly UV pigment/cones in the ventral part.

For the simulation, we have used the cone map provided by Jacobs in his book chapter (see references), from data by Szel, Rohlich, Caffe, Juliusson, Aguire, Van Veen, 1992 (see figure).

 Absorption spectra of the mouse's two photopigments (Jacobs, 2008) Possible repartition of cones on the mouse retina (from Szel, Rohlich, Caffe, Juliusson, Aguire, Van Veen, 1992)

In the Matlab simulation, we used rectangular arrays of cones, with M cones at the top, UV cones at the bottom and mixed cones in a central band (see figure). The mixed cones' spectra was obtained by interpolating linearly between the M and UV cones, to mimic a gradient of relative pigment concentration. This relies on the assumption that there is a linear relation between the pigment concentration and the spectrum, and that the spectra can be simply added.

 Repartition of cones in Matlab simulation Simulated spectra of mixed cones, by interpolation

#  Pixel (in pixelCreate.m)

The ISET pixels contain information about the pixels' size and spacing, and their noise sources.

Mouse cones have a size of about 2 um on average (photodetector width and height for ISET pixels). They are spaced about 9 um apart on average ("width" and "height" arguments in ISET pixels). The space between the cones is normally filled with small tightly packed rods, that we didn't model in this project.

The total mouse retina has about 180,000 cones. We simulated a full field of view of 125 degrees, with an array of 426x426 cones, for a total of 181,476 cones. For comparison, the human fovea has about the same number of cones in a field of view of a half degree.

With such a wide spacing, the mouse's cone vision must face a sampling problem : for a spatial frequency of 1 cycle/degree, there are only 3 or 4 cones per cycle. At 2 cycles/degree, there are only 1.5 to 2, and aliasing must start appearing in cone vision.

An ISET pixel can have different types of noise added to it. There is Poisson-distributed photon noise (or shot noise), and additional read noise and dark noise.

For our first measures, we used only photon noise, and tried adding read noise gradually (see results and discussion).

Another possibly important factor is the well capacity of the cones, that is the maximum number of photons they can absorb, which would mimic the saturation of real cones. We have used a value of 20,000 photons and a luminance in which saturation didn't occur, but the problem of saturation would need be better modelized.

The last value to set is the conversion gain, that gives the voltage output for one photon absorption. We used 1e-5. Because we only considered the eye down to the cones' output and not further, this value had little importance to us.

#  Results

We assembled the whole system and ran tests, to try to get a simulator as close as possible to the real mouse vision. We decided to measure this using frequency sensitivity experiments (see figure), that measure limit values of contrast and spacial frequency above which the animal perceives a sinusoidal grating as uniform gray. On this curve, we can observe that the cutoff frequency (above which the mouse always sees uniform gray, whatever the contrast) is before 1 cyc/degree.

 Frequency sensitivity curve (from Prusky, 2004)

Our first results (see figure) revealed that the two main types of cones received very different numbers of photons : the M cones received around 10 times more (on average 700 photons in 1ms for a stimulus scene of 300 cd/m2.). This resulted in a much feebler output from the UV cones (70 photons on average for the same experiment.).

 First results : different cones get different numbers of photons. The right figure is a rescaled version of the bottom part of the left figure. (field of view of 120 deg, spatial frequency of 1 cyc/deg, contrast of 100%, no noise apart from photon noise)

In a real retina, we would not measure such an output because the cones will adapt to the light level and output voltages in the same range of values. To simulate adaptation, we added a gain to the output of each type of cone, in order to get the same mean output over the whole retinal image (see figure). We can observe that the UV cones give a much noisier signal, since they have the same photon noise for 10 times less signal photons.

 Results after cone adaptation (field of view of 120 deg, spatial frequency of 1 cyc/deg, contrast of 100%)

Note that on this picture, the grating is clearly discernable. Since this experiment is at 1 cyc/deg, this means our simulated mouse has better vision that real mice, and that we should probably add noise.

We then proceeded to the simulation of cone outputs for different values of contrasts, at a given spatial frequency. We used a linear classifier (SVM with linear kernel) to distinguish between gratings and uniform images, and used the percentage of correct classifications to build a contrast sensitivity curve (see figure).

 Constrast sensitivity curve with fitted Weibull function (spatial frequency of 1 cyc/deg, contrasts from 0 to 10%)

We took the contrast threshold at 81% of correct results : we consider that contrasts higher than the threshold are correctly identified. The red curve on the figure is a Weibull function that we fit to the data in order to get a less noisy threshold value.

Using contrast threshold at each frequency, we built a frequency sensitivity curve (1/contrast threshold, as a function of frequency). Depending on the quantity of read noise that we added to the photon noise, we obtained different cutoff values of frequency and peak values of sensitivity. The figure displays the best curve, for read noise of 0.01 volts.

 Tentative frequency sensitivity curve (frequencies from 0.05 to 0.7 cyc/deg)

#  Discussion and future work

## Frequency sensitivity

The frequency sensitivity curve diplays satisfactory behavior of the eye simulator : the cutoff frequency is before 1 cyc/degree, the peak sensitivity is around 6.

The lowest sensitivity values are lower than 1 (implying a contrast higher than 100%), because the value is taken on the Weibull curve, whose accuracy is impacted by the large amount of noise on the contrast sensitivity curve for difficult classifications. We must also note that the final curve is overall very noisy. The results would need to be extended to a wider range of frequency and to be repeated several times to estimate the variance of the experiment, before we can really reach a conclusion and compare with the real mouse's performance. A more specific study of the noise sources would also be necessary.

The frequency sensitivity curve from Prusky shows that the mouse doesn't perceive above 1 cyc/deg. Analysis of out OTF shows that the optics don't seem to be the limiting factor : the mouse's optics allow good focus at higher than 1 cyc/deg, at least in certain wavelength ranges. The transmittance of the lens cuts out some photons, but there should still be enough in the M-cone's area of sensitivity. The coarse sampling of the cones limit the frequency, but there shouldn't be too many problems up to 1 cyc/deg. It could be that some information is lost in the brain circuits, that we don't account for. We also have to take into account that our classifiers are linear, whereas nothing indicates that the brain should be.

## UV vision and pigment repartition

Few mammals see in the UV (rodents especially seem to be able to do this.). The mouse's UV cones have a peak sensitivity in a range of wavelengths that is largely cut off by the lens, which gives a low signal-to-noise ratio, and where the optics add considerable blur. Therefore information from the UV range is largely lost, but the mouse must be able to get at least the general luminance. How the luminance in the UV spectrum is an evolutionary advantage remains unclear.

One possible advantage of having cones that get different amounts of photons could be a wider dynamic range : when the luminance is low, the M cones get many photons, and when it is high, the UV cones will get photons when the M cones saturate. We could go on to simulate saturation (by limiting the well capacity of the pixels/cones) to see if it is indeed the case. If yes, the mouse retina would act like two different sensors that get complementary information. Since the rods' peak absorption is in between the two pigment types (507nm for the human rod), maybe it could act as a link between the two, like the mixed pigments do.

The placement of the different cones is also strange : the mouse sees in the green range upwards (and frontwards), and in the UV range downwards(and backwards). Maybe is it useful to see predators in a certain frequency range and food in another...

## New experiments

To get a full sense of the mouse's vision, it would be useful to simulate rods. They cover a large part of the retina, and would help avoiding aliasing, which could play a role in frequency sensitivity. For this, it is important to get more precise data on the range in which the rods are efficient and saturate.

A whole different type of experiment would be color discrimination. We already have a reference curve from Jacobs, G. H., Williams, G. A., Fenwick, J. A. (2004). Influence of cone pigment coexpression on spectral sensitivity and color vision in the mouse. Vision Res 44, 1615–1622.

#  Sources and references

• From candelas to photoisomerizations in the mouse eye by rhodopsin bleaching in situ and the light-rearing dependence of the major components of the mouse ERG Arkady L. Lyubarsky, Lauren L. Daniele, Edward N. Pugh Jr, Vision Research 44 (2004) 3235–3251
• A SCHEMATIC EYE FOR THE MOUSE, AND COMPARISONS WITH THE RAT S. REMNLLA and P. E. HALLETT, Vision Res. Vol. 25. NO I. pp 21-31. 1985
• Visual adaptations in a diurnal rodent, Octodon degus, Jacobs, G. H., Calderone, J. B., Fenwick, J. A., Krogh, K., Williams, G. A. (2003). J Comp Physiol A 189, 347–361.
• Cone Pigments and Vision in the Mouse, Jacobs, G. H., chapter 16 of Visual Transduction and Non-Visual Light Perception, Humana Press, 2008
• Unique separation of two spectral classes of cones in the mouse retina, Szel, A., Rohlich, P., Caffe, A. R., Juliusson, B., Aguire, G., Van Veen, T. (1992). J Comp Neurol 325, 327–342.
• Characterization of mouse cortical spatial vision, Prusky, G. T., Douglas, R. M. (2004). Vision Res 44, 3411–3418.