Two-photon vision – Seeing colors in infrared

This review discusses the current state of knowledge regarding the phenomenon called two-photon vision. It involves the visual perception of pulsed infrared beams in the range of 850 – 1200 nm as having colors corresponding to one-half of the IR wavelengths. It is caused by two-photon absorption (TPA), which occurs when the visual photopigment interacts simultaneously with two infrared photons. The physical mechanism of TPA is described, and implications about the efficiency of the process are considered. The spectral range of two-photon vision is defined, along with a detailed discussion of the known differences in color perception between normal and two-photon vision. The quadratic dependence of the luminance of two-photon stimuli on the power of the stimulating beam is also explained. Examples of recording two-photon vision in the retinas of mice and monkeys are provided from the literature. Finally, applications of two-photon vision are discussed, particularly two-photon microperimetry, which has been under development for several years; and the potential advantages of two-photon retinal displays are explained.


Introduction
Vision begins with the physical process of absorption of photons by visual pigments embedded in the membranes of the outer segments of the photoreceptors.According to the principle of univariance, acts of chromophore isomerization are indistinguishable from each other; consequently, photoreceptors are color-blind (Rodieck, 1998).The sensation of color is encoded by comparing the chromophore isomerization rates occurring at the different types of photoreceptors.In other words, the number of isomerization events occurring at individual photoreceptors of a given type is transformed, through a very complex system of connections in the neural retina and visual cortex, into the perception of color.The two-photon vision phenomenon manifests this mechanism: humans see green color under the stimulation of their retina with a pulsed laser beam of wavelength 1000 nm.Under these conditions, the two-photon absorption events that occur mostly at M-cones activate vision (Palczewska et al., 2014).Moreover, this perception of color shifts with wavelengths from 850 nm to 1200 nm, practically recreating the whole rainbow in the near-infrared range (Dmitriev et al., 1979;Manzanera et al., 2020;Stachowiak et al., 2022;Marzejon et al., 2022;Komar et al., 2019).
Two-photon absorption is a well-known physical phenomenon with numerous applications, including two-photon microscopy (Denk et al., 1990).The fact that it can trigger vision was astonishing for me and my colleagues in 2014 (Palczewska et al., 2014).Two-photon absorption is a rare quantum event that requires high photon flux densities to be observed (Xu and Webb, 1996).Nevertheless, photoreceptors are neural cells highly specialized in photon detection.The absolute threshold for cone vision was recently estimated to be 2-5 photons per photoreceptor (Koenig and Hofer, 2011), and rods can detect even single photons (Pugh, 2018).Because of their superior sensitivity, photoreceptors can respond to two-photon absorption events, especially when short pulses and high laser repetition frequency increase the efficiency of the process.We are used to thinking that vision has evolved to increase the chances of survival.However, it is unlikely that two-photon vision can occur under natural conditions.Nevertheless, this limitation does not mean it is a curiosity, as its specific properties can be used in novel retinal displays or for medical diagnostics.
Since 2014, knowledge of two-photon vision has increased significantly and a new area of research has emerged.The purpose of this review is to summarize this field and outline directions for its future development.
physicists for almost a century.It was first predicted theoretically in 1931 by Maria Göppert-Mayer in her doctoral dissertation (Göppert-Mayer, 1931).Already at that time, she pointed out that high light intensities would be needed to observe this process.2PA occurs when an atom or molecule interacts simultaneously with two photons, so large photon fluxes are needed to detect the macroscopic effects of such a rare event.Only with the invention of lasers did such high photon fluxes become practically possible.The first experimental evidence that 2PA occurs was provided by W. Kaiser and C.G.B. Garret in 1961; they measured 425-nm fluorescence from a CaF 2 :Eu 2+ crystal induced by a 694.3-nm ruby laser beam (Kaiser and Garrett, 1961).It is important to note that the observed fluorescence resulted from a second process, spontaneous emission, which occurred after the earlier 2PA.Further development of lasers enabled the development of spectroscopic techniques based on 2PA (Friedrich and McClain, 1980).Early applications of 2PA spectroscopy also included studies of the visual chromophores (Birge, 1986;Birge et al., 1982).When the scanning laser microscope was invented (Sheppard, 1980;Davidovits and Egger, 1971;Davidovits and Egger, 1969) and femtosecond lasers were available (Moulton, 1986), it was possible to excite a 2PA in a biological sample efficiently enough to produce such strong fluorescence to obtain a microscopic image of the sample.The technique was called two-photon microscopy and became one of the most valuable and powerful tools in biological imaging (Denk et al., 1990;Xu and Webb, 1996;Helmchen and Denk, 2005;Xu et al., 1996;Zipfel et al., 2003).
Denk, Strickler and Webb, the inventors of two-photon microscopy, provided the relationship which links the number of photons (N a ) absorbed by the fluorophore per laser pulse (equation (1) (Denk et al., 1990): where σ 2ph is the two-photon cross section (measured in cm 4 ⋅s); 〈P〉 is the average incident laser power; τ p and F p are pulse duration and repetition frequency of the laser, respectively; NA is the numerical aperture of the microscope objective; ℏ is the reduced Planck's constant; c is the speed of light; and λ is the laser wavelength.Equation (1) assumes paraxial approximation and squared shape of the laser pulses.Denk, Piston, and Webb later provided a more general version of this relationship, for laser pulses of any shape (equation (2) (Denk et al., 2006): where ξ = 〈P 2 〉 〈P〉 2 , is a factor dependent on pulse shape; for Gaussian pulses, ξ ≅ 0.664 τpFp ; and ξ ≅ 0.558 τpFp for hyperbolic-secant pulses, called "two-photon advantage" in (Denk et al., 2006).
Both equations show several important aspects of 2PA, which influence both two-photon microscopy and two-photon vision: (1) a quadratic relationship with average laser power; (2) an inverse dependence on pulse length and repetition frequency of the laser; (3) a strong dependence on NA.All these aspects of two-photon vision are discussed in detail (see below).
Photons from a laser beam transfer their energy to any irradiated biological sample (usually containing many different interacting molecules with a vast number of energy bands and levels) not only by 2PA but more likely by one-photon absorption (1PA).In the latter case, some absorbed energy will be emitted as fluorescence at longer wavelengths than the excitation beam, but most will be converted into heat.The heat that accumulates when the sample is irradiated with a continuous laser beam may lead to sample damage.Therefore, it would be challenging to obtain two-photon excited fluorescence (and a two-photon vision effect) from a biological sample using a continuous beam.On the other hand, if all the photons from the beam were delivered within a very narrow time interval, it would not only increase the chance that a chromophore molecule would interact with two photons at once but also, while the pulse is off, the excess of heat would be safely transferred to the environment.Let us consider, for example, a femtosecond laser with a pulse duration of 200 fs and a repetition rate of 80 MHz.In this case, the interval between pulses is 12.5 ns, 16 thousand times longer than the pulse duration.For the vast majority of the time, no photons interact with the sample molecules, and energy is not delivered.Therefore, by using short pulses, the risk of thermal damage is minimized, while 2PA is favored.The limiting factors for shortening of the pulse are risk of damage due to nonlinear effects, such as self-focusing and plasma formation; and pulse broadening in the sample due to group velocity dispersion (GVD).
According to Denk et al. (Denk et al., 2006), the total absorbed power P a in the 2PA process can be calculated as follows (equation (3): where C is the chromophore concentration and n is the refractive index.Two-photon vision is the visual perception of light resulting from isomerization of the visual pigment caused by two-photon absorption (Palczewska et al., 2014).Similarly to two-photon microscopy, there is excitation of the visual pigment due to 2PA.Unlike two-photon microscopy, however, there is no requirement for occurrence of the latter process; i.e., emission of visible-range radiation.The vision is triggered directly due to isomerization of the visual pigments caused by 2PA.This process is depicted schematically in Fig. 1.
In two-photon vision, the human eye plays the role of the microscope objective, as in the case of retinal imaging techniques such as Scanning Laser Ophthalmoscopy (SLO).Nevertheless, optical aberrations significantly limit the human eye's focusing capabilities; e.g., optimal lateral resolution was found for a pupil size of 2.5 mm (Donnelly and Roorda, 2003).For larger beam diameters, it is necessary to use adaptive optics corrections to achieve diffraction-limited spot size at the retina.Therefore, in practice equations (1) and (2) for stimulating beams with diameters greater than 2.5 mm (or NA greater than 0.09) are unlikely to be satisfied for the human eye, without AO correction.

History of two-photon vision
In 1965, Vasilenko et al. published the first report on the perception of pulsed NIR light resulting from an unknown process (Vasilenko et al., 1965).They observed color associated with the second-harmonic of directly viewed 5-ms pulses of Ne emission lines (948.6 nm, 1114.3 nm, 1117.7 nm, 1152.5 nm, and 1179 nm) from a Ne-H 2 gas mixture.While the first line (948.6 nm) was perceived as red light, the four longer wavelengths were perceived as yellow-green, yellow, orange, and orange, respectively.Eleven years later, Sliney et al. provided a detailed analysis of this phenomenon on the basis of visual threshold measurements for various light sources (Sliney et al., 1976).The authors concluded that visual response to the pulsed NIR light does not stem from "normal photochemistry of vision," suggesting second harmonic generation (SHG) in the retina as the explanation of their observations.The problem was researched further by Dmitriev et al. (1979).Their study was based on color matching for a OPO (Optical Parametric Oscillator) beam and incandescent lamp emission, spectrally filtered by an adjustable monochromator.The results revealed that the color of infrared beams substantially differed from the color of the second harmonic; wavelengths shorter than 1000 nm were blue-shifted, while longer wavelengths were red-shifted.They proposed that the phenomenon is caused by two-photon absorption occurring in visual pigments.They also suggested that observed deviations of color may be explained by distortion of their two-photon absorption spectra compared to the one-photon process.However, their results were not fully convincing for the scientific community.Zaidi and Pokorny, in 1988, argued that the SHG in the cornea is the best explanation of the published observations at the time (Zaidi and Pokorny, 1988).In the first decade of the 21st century, there were two new reports on visual observations of infrared beamsboth emanating from groups using Nd:YAG lasers of ns-pulses scattered from samples of roughened surfaces (Kazakevich et al., 2006;Theodossiou et al., 2001).The authors observed speckle patterns that were perceived as green, although they originated from an infrared beam.The patterns disappeared after placing a filter that attenuated the infrared beam between the eye and the sample.Different explanations were in the two reports; namely, SHG in the cornea (Theodossiou et al., 2001), and SHG in periodic retinal structures (Kazakevich et al., 2006).This long-term controversy was resolved after publication of a study by Palczewska et al. (2014).This report combined the results of several types of experiments (psychophysical studies on humans, ex-vivo transretinal ERG recordings from mice, and spectral analysis of two-photon bleaching of pure rhodopsin crystals) with quantum mechanical modeling of two-photon activation of rhodopsin.The overall analysis of the data convincingly showed that two-photon isomerization of visual pigments was possible under each of the experimental conditions studied, and 2PA is the best explanation of all of the experimental evidence.Further research confirmed that the retina is where this phenomenon occurs -the cornea and lens were ruled out as its origin (Artal et al., 2017;Doyle et al., 2023;Gorczynska et al., 2022).

Spectral range and efficiency of two-photon vision
The eye's spectral sensitivity does not abruptly terminate after 700 nm, the border of the so-called visible range.Data in the literature support sensitivity up to 1000 nm (Goodeve, 1936;Griffin et al., 1947;Walraven and Leebek, 1963).There is a linear decrease in the logarithm of the eye's sensitivity with decreasing radiation frequency (photon energy) (Griffin et al., 1947), corrected for water absorption in this region (Walraven and Leebek, 1963).Therefore, infrared beams used for retinal imaging in SLO and OCT systems can be seen; the visual threshold at the fovea corresponds to a 800-nm beam, 4⋅10 6 higher than for a 555-nm beam, and 2⋅10 7 higher for a 850-nm beam (Walraven and Leebek, 1963).Because of the higher sensitivity of L cones over M cones (Stockman and Sharpe, 2000;Stockman et al., 1993), visual perception in this region manifests as a red color.A reverse color perception effect for the 800-900 nm range is also noted (Brindley, 1955); as the wavelength increases, the color attributed to the light shifts toward orange rather than toward deeper red.
Nevertheless, the visual thresholds, expressed in average power, for pulsed infrared beams focused on the retina begin to stabilize and even decrease around 900 nm (Palczewska et al., 2014;Dmitriev et al., 1979;Manzanera et al., 2020;Sliney et al., 1976).The relative sensitivity of the retina (the ratio of the visual threshold for 555 nm to the visual threshold for a given wavelength) shows significant deviations from the decrease in sensitivity predicted in the literature (Fig. 2 a) (Palczewska et al., 2014).Color perception also changes in this spectral region.The sensation of color of the stimulus corresponds to half-of-the wavelength of the stimulating beam.
In Fig. 2 b) there are combined results of two separate experiments, reported in (Manzanera et al., 2020;Stachowiak et al., 2022).Stachowiak et al. measured visual thresholds at the fovea for three healthy dark-adapted volunteers with a tunable fiber laser and well-defined pulse train parameters in the range 872-1075 nm.The volunteers perceived the three shortest wavelengths (872, 893, and 914 nm) as a mixture of red and blue.The blue-colored sensation disappeared when the power of the laser beam was close to the absolute visual threshold; then the beam appeared to be red only.Therefore, two distinct visual thresholds were measured in this region: the higher one, connected with the disappearance of blue, and the lower one, associated with the disappearance of red color, which was an absolute threshold of vision in this region.The assumption was made that these lower thresholds were the thresholds of normal, one-photon vision.The sensitivities calculated as the inverse of these thresholds (red circles in Fig. 2b) were matched with the sensitivity curve of Walraaven and Leebeek, which is shown as the black solid line.The validity of this matching was confirmed further by measuring the visual threshold in the same system with a 520-nm cw laser for the same volunteers and comparing the values obtained with the Walraaven and Leebek curve (not shown in Fig. 2b).The visual thresholds connected with blue sensation were interpreted as thresholds of two-photon perception, and respective sensitivities are shown with green circles in Fig. 2b.For wavelengths starting at 950 nm and above, only one visual threshold existed; and the beam was perceived as having half-of-the-wavelength color: blue for 950 nm, green around 1000 nm, and green-yellow for 1075 nm.In this region, two-photon perception became dominant for this laser as being more effective than one-photon perception.It is important to note that efficiency of two-photon vision depends on laser pulse train parameters, according to equations (1) and (2); therefore, two-photon sensitivity calculated on the basis of the average power of the laser beam, depends on these parameters as well.Manzanera et al. also measured visual thresholds at the fovea center for four healthy volunteers with the supercontinuum laser in the 850-1100 nm range (Manzanera et al., 2020).Perception of two colors was reported in this case as well, red and blue for the wavelengths 850, 880, and 900 nm.The authors measured only two-photon visual thresholds, linked to the perception of half-of-the-wavelength color and expressed them as average power at the cornea.The two-photon visual thresholds obtained for two repetition frequencies of their laser source differed from each other, but this differences is expected due to the physical nature of the two-photon absorption; and the data agree well with the theoretical model provided in their paper (Manzanera et al., 2020).To compare the results of both experiments, their visual thresholds were recalculated to sensitivities and scaled to the Waalraven and Leebeek curve by taking into account the fact that only the three shortest wavelengths were perceived by both vision mechanisms.Actually, the model quite well defines the position in the graph of relative sensitivity, because for both frequencies the points for the three shortest wavelengths should appear below the Waalraven and Leebek curve.The most efficient source for two-photon vision was the super continuum with the lowest frequency (1.98 kHz), which is expected according to equation (1).Recently, Marzejon et al. provided a more detailed discussion of the theoretical model of the dependence of two-photon visual thresholds on the pulse train parameters of the laser (Marzejon et al., 2023).It follows from this model, that the differences in two-photon sensitivities between lasers will disappear after multiplying the sensitivities by the square root of the duty cycle of the lasers; i.e., the product of the pulse length and laser frequency (neglecting the pulse shape differences).After such a calculation, the results from both papers presented in Fig. 2b overlap.Nevertheless, presenting the data as in Fig. 2., with sensitivities calculated from the average power is of practical importance; it is the average power of the pulsed beam that is measured in the experiment, and it shows the importance of the pulse train parameters for two-photon vision efficiency.

The colors of two-photon beams
The colors of two-photon beams were investigated in several studies so far (Palczewska et al., 2014;Dmitriev et al., 1979;Kazakevich et al., 2006;Doyle et al., 2023;Gil et al., 2023), and results of these investigations are gathered together in Fig. 3. To date, the shortest wavelength documented in the literature for which two-photon perception has taken place is 850 nm, as indicated in Fig. 2b.However, it is difficult to unambiguously determine the 2P-color for wavelengths below 900 nm, because both mechanisms of vision coexist in this region and perceived color is purplea mixture of blue and red (Stachowiak et al., 2022;Doyle et al., 2023;Gil et al., 2023).Therefore, matching of single monochromatic wavelengths to two-photon colors was performed successfully for wavelengths above 900 nm.With the exception of Dmitriev's historical measurements, all matched wavelengths on Fig. 3 lie above the double frequency line.The colors of twophoton beams seem to be shifted to longer wavelengths than the corresponding second harmonic; and this shift is more pronounced for the shorter wavelength part of the spectrum (900-920 nm/480 nm) and its central part (1020-1060 nm/530-560 nm).The second region of the deviation coincides with the maximum of the hue-discrimination curve (Wright and Pitt, 1934), which gives it additional credibility.However, the reason for this deviation remains unknown so far.Hypothetical explanations are discussed below, the verification of which requires further research in the future.(Walraven and Leebek, 1963).The data obtained for two-photon perceived laser pulses are depicted with symbols.Sensitivities were calculated based on visual thresholds expressed in terms of average beam power at the cornea in reference to the maximal foveal sensitivity at 555 nm.a) Visual sensitivities for two healthy volunteers S1 (squares) and S2 (circles), with the same laser source upon modification of pulse length due to dispersion in a 1-km-long optical fiber.Red symbols indicate data obtained for pulses of the order of 1 ps; black symbols for pulses stretched in fiber to 0.3-0.6 ns.Sensitivities for 800 nm, perceived due to one-photon vision, were assumed as equal to normal eye sensitivity for this wavelength (Walraven and Leebek, 1963).Data adopted from (Palczewska et al., 2014).b) Average one-photon and two-photon sensitivities for 3 volunteers measured with the system described in (Stachowiak et al., 2022) are depicted with red and green circles; error bars equal to 1 standard deviation.Average two-photon sensitivities measured for 4 healthy volunteers with the system described in (Manzanera et al., 2020) are indicated by orange squares and blue triangles; error bars equal to 1 standard deviation.Data adopted from (Manzanera et al., 2020;Stachowiak et al., 2022).Detailed description in text.One possible explanation is the difference in the degree of excitation of photoreceptor types between one-and two-photon vision, which, according to the principle of unitarity (Rodieck, 1998), could manifest itself in a shift in color perception relative to normal vision.
There are at least two premises in the current literature that support this unitarity idea.The first relates to differences in the shape of the dark adaptation (DA) curve (Lamb and Pugh, 2004) obtained for the test stimuli perceived, due to one-and two-photon vision (Ruminski et al., 2019).Although both stimuli were perceived as green, the same retinal location was tested in the same person, and prior bleaching of the retina with white light was also equal; but the dark adaptation curves have a different shape -Fig.4(a).
The rod-cone break occurs later for the two-photon stimulus (red circles, 1040 nm), and the cone plateau is less elevated from the rod plateau in this case.The shape of the DA curve can be interpreted in such a way that the difference between the plateau of the cones and the plateau of the rods for a given wavelength corresponds to the difference in the sensitivity of the rods (scotopic) and the cones (photopic) for that wavelength (Kalloniatis and Luu, 1995).Less difference registered for two-photon stimuli suggests that the advantage in sensitivity of rods over cones is not as great for two-photon vision as for one-photon vision.Relatively, the rods would be stimulated less than cones, and twophoton vision would be more cone-ish.
A similar conclusion can be drawn from the results of the investigation of the pupillary light reflex (PLR) induced by two-photon vision (Fig. 4b).The PLR was tested for 14 healthy volunteers, with 520 nm and 1040 nm stimuli (Zielińska et al., 2019).The perceived brightness of the stimuli were carefully matched for each subject with a separate psychophysical procedure.Despite this adjustment, the PLRs caused by the two-photon stimulus were considerably weaker than those by the onephoton stimulus: minimum pupil diameters were bigger and constriction velocities were smaller, and the time of maximum constriction was shorter (Zielińska et al., 2019).Due to the low brightness of the stimuli, the participation of ipRGC (intrinsic photosensitive Retinal Ganglion Cells (Münch and Kawasaki, 2013) in the formation of the pupillary response was unlikely and for the short-duration and low-intensity stimuli, rod photoreceptors contribute mostly to the minimum pupil diameter (McDougal and Gamlin, 2010;Kostic et al., 2016).Thus, relatively less stimulation of rods in two-photon vision may explain the smaller PLR registered for the two-photon stimulus.
The degree of stimulation of cones and rods in two-photon vision is interesting from the scientific point of view and certainly worth further studies.Indeed, if one takes the differences in color perception, the shape of the DA curves, and the weaker PRL as premises leading to the conclusion that two-photon absorption occurs more efficiently in cones than in rods, what could be the reasons for this?One explanation might be higher two-photon absorption cross section (σ 2ph ) of the cone pigments in comparison to rhodopsin.Another explanation could relate to the waveguiding properties of the cone inner segments, which might increase the local flux density at the cone outer segments and lead to a higher probability of two-photon absorption.
Two-photon fluorescence emission from endogenous retinal  fluorophores may be a competing hypothetical explanation for the observed redshift in the perceived color of two photon vision.Given the extreme sensitivity of photoreceptors and the proximity to the site of this fluorescence, it seems possible that even a minute contribution of such light could account for the observed color perception bias.In particular, if there were a fluorophore emitting in the red range of the spectrum (above 600 nm), it could explain the shift in perception toward longer wavelengths.The best-known candidate is ocular lipofuscin and its major component, A2E, whose emission maximum lies in the range 600-650 nm (Lamb and Simon, 2004).Lipofuscin accumulates in the retinal pigment epithelium (RPE), which is near photoreceptors.However, the excitation spectrum of lipofuscin shows a maximum of around 470 nm (Boulton et al., 1990), but the most significant redshift in twophoton vision was observed for 1040-1080 nm, corresponding to singlephoton excitation at 520-540 nm.Lipofuscin fluorescence could therefore account for the observed shift in the 900-950 nm region, but not likely in the 1000-1100 nm region.Ocular melanin has two absorption bands, the longer of which overlaps with the A2E band, around 470 nm, and emits below 600 nm (Palczewska et al., 2023).Other candidates are retinoids, but their excitation spectra show maxima for wavelengths shorter than 400 nm, and emissions occur in the blue-green range (Takemura et al., 1980).Other endogenous fluorophores, such as NADH, flavin (FAD), elastin, and collagen, have excitation and emission ranges similar to retinoids (Takemura et al., 1980).Further research and more data on two-photon color perception are definitely needed to test the hypotheses discussed above regarding the causes of observed redshift.

The quadratic dependence of stimulus brightness on power
Two-photon absorption depends quadratically on the average power, as can be seen from equations ( 1) and ( 2).Therefore, the brightness of two-photon stimuli also depends on the square of the power of the stimulating beam.The difficulty in demonstrating this effect is that there is currently no way to directly measure the brightness of two-photon stimuli, because two-photon luminance curve does not exist.Therefore, brightness is determined by comparing two-photon stimuli with one-photon stimuli (Doyle et al., 2023;Zielińska et al., 2019).Such a procedure has been proposed and tested in (Zielińska et al., 2019).Thus, two rings (520 nm and 1040 nm) of 3.5-deg diameter generated by fastlaser scanning were projected simultaneously on a subject's retina (see inset in Fig. 5a).The 1040 nm power was predefined in the task, and the 520 nm power was adjusted by the subject to obtain the impression of the same brightness.The 1040 nm wavelength is perceived as having a color of 530-560 nm, according to Fig. 3, so the differences in color between the two beams, reported by the subjects, made this task difficult to some extent.Nevertheless, the results (in Fig. 5a) show that the power dependence of the two-photon beam luminance is strongly superlinear (the power of the VIS stimulus represents the perceived luminance, which in this case is linearly dependent on the VIS power, since the size and shape of the VIS stimuli are constant).The deviation from the expected 2.0 slope in the log-log plot shown may have been caused by the different colors of the stimuli.
Another way of showing the quadratic dependence of two-photon brightness on the power was performed by Ruminski et al. (Ruminski et al., 2019), and is presented in Fig. 5 b.The differential thresholds, VIS (520 nm) and IR (1040 nm), for ring stimuli of 0.4-deg diameter were measured on the same background of 505-nm wavelength, with increasing luminance.The log-log plots created from these data exhibited slopes around 2.0 for three tested subject, indicating nonlinearity of two-photon vision (Ruminski et al., 2019).

Two-photon perception in other species
An important part of two-photon vision studies are ERG recordings on mice and primates (Palczewska et al., 2014;Vinberg et al., 2019;Gaulier et al., 2022;Gaulier et al., 2021).The two-photon transretinal ex vivo ERG responses of isolated mice retinas upon irradiation of 730-1000 nm wavelengths (80 MHz, 75 fs) were registered and analyzed for the first time in (Palczewska et al., 2014).The photoreceptors were directly exposed to the NIR laser beam, so the possibility of generation of a second harmonic from the cornea and lens was excluded.The retinas of the investigated wild-type mice exhibited responses attributed to the rods for all of the applied wavelengths of the stimulating beam.As in humans, responses for 900-nm and 1000-nm wavelengths were greater than predicted by one-photon NIR stimulation (Fig. 6a).Moreover, the values of factor n, calculated from the modified Naka-Rushton equation (Palczewska et al., 2014;Nymark et al., 2005), which relates normalized response amplitude to the energy of the stimulus, increased with the stimulation wavelength from values close to 1.0 for 730 nm to 1.8 ± 0.2 for 1000 nm (Fig. 6a).The increase in n can be understood as the increase of the contribution of the nonlinear process (two-photon absorption) to the recorded response.These initial findings were confirmed in mice, and later expanded to primates with an improved specimen holder, allowing for simultaneous two-photon Fig. 5. Log-log plots indicating the quadratic dependence of two-photon brightness (luminance) on the power of the stimulating beam.a) The power of the 520 nm (VIS) stimulus was matched to that of the 1040 nm (IR) stimulus by 14 healthy volunteers to obtain the same luminosity.The mean of the matched VIS powers are indicated by black squares, where error bars correspond to 1 SD (standard deviation of the mean).Linear fits to the data are indicated by the red line (to the mean values) and the gray lines (to the data for each subject).Inset: subject's view during the brightness adjustment: 1040 nm and 520 nm stimuli are visible as two adjacent green rings of 3.5-deg diameter, and fixation as the red dot.The figure is reprinted from (Zielińska et al., 2019).b) The visual thresholds for the 520-nm (VIS) and 1045-nm (IR) stimuli were measured on the same, increasing, backgrounds by three healthy volunteers (S1, S2, S3).The background luminance ranged from 0 to 1.8⋅10 3 photopic Trolands.The slopes of fitted lines for each subject are indicated.Figure reprinted with permission from (Ruminski et al., 2019) © Optical Society of America.
imaging and ERG recording (Vinberg et al., 2019).As previously, the retinal samples were stimulated with 730-1000 nm beams (80 MHz, 75 fs).Gnat1 -/-and wild-type mice, as well as a foveal region of the macaque's retina, were used as models of cone, rod, and cone responses, respectively.The sensitivities calculated from the recorded responses are shown in Fig. 6b.The responses for wavelengths below 800 nm coincide well with the one-photon perception model, as indicated with dashed lines.Responses for the three longer wavelengths deviate from the model, indicating two-photon-based visual perception.In agreement with the findings from humans (discussed in the above paragraph), cone recordings are substantially higher than those from rods.
The ERG responses induced by nonlinear interaction of visual pigments with pulsed light were also investigated by Gaulier et al. (Gaulier et al., 2022;Gaulier et al., 2021).The authors of (Gaulier et al., 2021) designed a pump-probe experiment on rhodopsin, with the retina of a living mouse as a detector.They compared how ERG responses of the mouse retina depend on different delays between pump and probe laser pulses, and were able to show that modification of the spectral phase of the pulses altered the A-wave of the registered electroretinogram.The other study (Gaulier et al., 2022) was devoted to characterization of the effect of various parameters of the pulsed laser (pulse duration, energy, focal spot size) on the ex vivo ERG response of the retinas from mice and living animals.

Applications of two-photon vision: Two-photon microperimetry and the visual displays
Microperimetry is a more advanced version of automated perimetry (visual field testing), which is a well-established functional vision test (Crossland et al., 2012).One of the main applications of perimetry is tracking the progression of glaucoma and other retinal diseases that lead to deterioration of photoreceptor function, such as age-related macular degeneration (AMD), diabetic retinopathy, geographic atrophy, or Stargardt's disease.In microperimetry, the functional test is accompanied by simultaneous acquisition of retinal images, which provides clinically relevant information, including the actual area tested and valuable statistics on the eye's fixation during the examination.This approach significantly increases the real spatial precision and provides an opportunity to test visual sensitivity in a small area of the impaired retina.
Two-photon microperimetry (TPMP) can have basically the same features as classical microperimetry, with one significant difference; namely, the stimulus for testing visual sensitivity is perceived via twophoton vision.The main advantage of using two-photon stimulation instead of normal, one-photon visual perception is the quadratic dependence of brightness on power in two-photon vision.This unique feature results in a smaller range of transient powers, between "completely unseen" and "definitely seen," than for normal vision.The range of uncertainty of visual perception is the range of the psychometric-function slope, as shown in Fig. 7 a.On the abscissa, there is stimulus intensity (understood as brightness) on a logarithmic scale, so quadratic dependence of brightness on power in principle leads to a twice narrower psychometric function for two-photon vision than for normal vision, as shown by Ruminski et al. (Ruminski et al., 2019).A narrower psychometric function has practical implications for perimetric testing, making the examination more reliable and consistent.
Since the determination of the visual threshold is inherently subject to less uncertainty, the repeatability of the test can be as much as twice better.This improvement was documented in (Ruminski et al., 2019) by repeated measurements of two-photon and one-photon sensitivities on 17 healthy volunteers, and it is represented as Bland-Altman repeatability plots in Fig. 7 b.The spread of the obtained results was significantly smaller for two-photon vision than for normal vision: 2.2 dB and 3.4 dB, respectively.As it produces less scattered results, TPMP has the potential to be a functional test for precise tracking of treatment progress; and it has the diagnostic capability of earlier detection of slight deviations from the norm.The lower variability of two-photon microperimetry in comparison to other methods based on visible spectrum stimuli was confirmed further in other studies (Łabuz et al., 2022;Mehta et al., 2022;Wei et al., 2021).Initially, two-photon sensitivities of the macula were tested, with a clinical version of a two-photon microperimeter, on a normal population and on patients with cataract, AMD, and diabetic retinopathy (Łabuz et al., 2020) -Fig.7c).The sensitivities of patients with impaired retinal function differ significantly from those of healthy patients.In contrast, sensitivities of patients with cataracts do not.This difference can be explained by better penetration of infrared light in the cataract lens, which is a highly absorptive medium for visible radiation but less absorptive for infrared.The last advantage of TPMP was investigated in two clinical studies performed before and after cataract surgery (Mehta et al., 2022;Komar et al., 2021).In one study (Komar et al., 2021), a two-photon laboratory perimeter measured the changes in visual green (based on mouse cone M pigment template, 508 nm); and red (a mix of 85 % macaque M-pigment (530 nm) and 15 % L-pigment (560 nm)) (Govardovskii et al., 2000).Figure reprinted from (Vinberg et al., 2019); with permission from Elsevier.sensitivity for a cohort of 32 patients.The changes for stimuli produced by 520 nm and 1028 nm laser beams were equal to 6.6 dB ± 1.3 dB and 2.8 dB ± 0.7 dB, respectively.The smaller variation for 1028 nm confirmed that the two-photon visual sensitivity was less distorted by cataracts than the one-photon visual sensitivity.In the same study, classical microperimetry with a MAIA device was performed.Surprisingly, the variation registered by MAIA were similar to those for the 1028 nm stimulus, 2.0 dB ± 0.6 dB.However, the differences between the two devices were too substantial to compare fairly.First, in MAIA, a white LED is used for stimulus projection (Pfau et al., 2021); and the 520 nm laser was probably more absorbed by cataractous lenses than broadband white-yellow light from an LED.Second, the MAIA device, being the final clinical product, was more ergonomic, and thus, it facilitated the measurements for patients with cataracts.Thus, the results from MAIA before and after cataract surgery could be generally more similar.The second report (Mehta et al., 2022) is based on the case of a 51-year-old male.The visual sensitivity of this patient before and after cataract removal was tested by a two-photon microperimeter with 520-nm and 1045-nm lasers and a NIDEK MP-3.In this case, the smallest variation was found for the 1045 nm laser (3.4 dB), while the variations for the 520-nm laser and conventional microperimetry were similar, 17.4 dB and 18 dB, respectively.The NIDEK MP-3 uses an LCD display for stimulus projection (Pfau et al., 2021).Both studies indicated that the light spectrum used for stimulus projection is the most critical factor for determining visual sensitivity before cataract removal.Thus, twophoton infrared stimulation would be the ideal tool for situations when examining the sensitivity of the retina is clinically meaningful before cataract removal surgery can be performed.
Additional examples of clinical TPMP applications include separate examinations of 28 patients with diabetic retinopathy (Łabuz et al., 2021), 23 patients with AMD (Łabuz et al., 2022), and 32 with glaucomatous neuropathy (Łabuz et al., 2022).The diabetic patients with retinopathy have significantly lower two-photon sensitivities (11.6 ± 2.0 dB) than healthy patients (15.5 ± 1.3 dB) (Łabuz et al., 2021).The two-photon sensitivities of AMD patients were compared with their visual sensitivities obtained by conventional microperimetry.Both types of sensitivities for this group were significantly lower than those for a normal population, but two-photon data displayed a smaller variation, which confirms the previously mentioned advantage (Łabuz et al., 2022).The TPMP proved also to be more sensitive in detecting glaucomatous neuropathy and provided a higher correlation with morphological changes at the retina than conventional microperimetry (Łabuz et al., 2022).
Considering the prospects for future development of TPMP, it is worth mentioning the cost, size, and inconvenience of using high-power pulsed-laser systems in the clinic.Therefore, it has been shown that much cheaper and more convenient picosecond fiber lasers can also be used for TPMP (Marzejon et al., 2023).The pulse lengthening from femtoseconds to picoseconds can be compensated for by the reduced repetition rate.As shown in Fig. 7 d, two-photon scotopic sensitivity maps obtained for healthy subjects have the same shape when obtained with the picosecond laser as does the map for the femtosecond laser.The visual thresholds are located a reasonable distance from the MPE level, ensuring that TPMP testing with the picosecond laser will be possible even in the diseased population.
Two-photon vision also has the potential to be adopted for visual retinal displays.There are several potential advantages of such displays: (1) only focused radiation is perceived, because the scattered infrared photons do not induce visual perception (Ruminski et al., 2019); (2) two-photon vision is less affected by ocular media opacities, and has increased absorption in aged lens (Ruminski et al., 2019;Łabuz et al., 2020); (3) combining retinal visual display with retinal imaging functionality (as in microperimetry, for example) would be easier due to lack of longitudinal chromatic and transverse aberrations between the imaging and stimulating beams (Doyle et al., 2023); (4) the quadratic dependence of brightness on power (Ruminski et al., 2019;Zielinska et al., 2022) offers the possibility to achieve better contrast; (5) more intense blue colors (Stachowiak et al., 2022), because the infrared radiation of wavelength 950 nm, perceived as blue, is not absorbed by macular pigment.
The strong dependence on NA, as predicted by equations ( 1) and (2) may cause significant differences in brightness between beams of different diameters (Zielinska et al., 2022).The natural eye aberrations prevent the use of full NA of the eye to increase the brightness of twophoton beams.Recently it was shown that aberration correction with an adaptive optics system can provide up to a 25-fold increase in luminance of a two-photon stimulus (Doyle et al., 2023).The control of the eye's optical aberrations provided by adaptive optics opens up a new field of exploration in two-photon vision research.

Conclusions
Although two-photon vision was observed for the first time in the 1960 s, it remained a curiosity with an unexplained mechanism for the next 50 years.Since its basis was explained in 2014, the field has grown significantly, and research has accelerated in recent years as more groups are interested in the effect.
This review provided an overview of the state of knowledge about this process and its potential applications.Two-photon microperimetry, an evolving technology, has great potential to become a more reliable and consistent technique for functional vision testing due to its better repeatability than conventional methods.On the other hand, the inherent properties of two-photon vision may be used for designing retinal displays with excellent contrast and color palettes.

Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Fig. 1 .
Fig. 1.The comparison of one-and two-photon vision mechanisms.a) In one-photon vision (normal vision), the retina is illuminated by light from a visible part of the spectrum (400-700 nm), and the visual chromophore isomerizes due to the one-photon absorption (1PA) process.b) Two-photon vision occurs upon irradiation of the retina by a pulsed NIR laser beam, and the isomerization of 11-cis retinal occurs due to the two-photon absorption (2PA) process.

Fig. 2 .
Fig. 2.Relative sensitivity of the fovea for pulsed infrared beams perceived due to two-photon vision.A classical foveal sensitivity curve for one photon vision is shown with black solid lines(Walraven and Leebek, 1963).The data obtained for two-photon perceived laser pulses are depicted with symbols.Sensitivities were calculated based on visual thresholds expressed in terms of average beam power at the cornea in reference to the maximal foveal sensitivity at 555 nm.a) Visual sensitivities for two healthy volunteers S1 (squares) and S2 (circles), with the same laser source upon modification of pulse length due to dispersion in a 1-km-long optical fiber.Red symbols indicate data obtained for pulses of the order of 1 ps; black symbols for pulses stretched in fiber to 0.3-0.6 ns.Sensitivities for 800 nm, perceived due to one-photon vision, were assumed as equal to normal eye sensitivity for this wavelength(Walraven and Leebek, 1963).Data adopted from(Palczewska et al., 2014).b) Average one-photon and two-photon sensitivities for 3 volunteers measured with the system described in(Stachowiak et al., 2022) are depicted with red and green circles; error bars equal to 1 standard deviation.Average two-photon sensitivities measured for 4 healthy volunteers with the system described in(Manzanera et al., 2020) are indicated by orange squares and blue triangles; error bars equal to 1 standard deviation.Data adopted from(Manzanera et al., 2020;Stachowiak et al., 2022).Detailed description in text.

Fig. 3 .
Fig. 3.The colors of single wavelengths perceived by one-photon vision matched to two-photon perceived stimuli.The symbols represent mean matched wavelengths with corresponding measurement errors: black squares with ± 5-nm error bars representing method accuracy(Dmitriev et al., 1979), red circles with error bars equal to 1 standard deviation (SD) from 30 matches(Palczewska et al., 2014), blue triangles with error bars representing the midrange of the dominant wavelength values(Gil et al., 2023), green diamond with error bars equal to 1 SD from 5 matches(Doyle et al., 2023), orange inverted triangle with error bars equal to 1 SD from 6 matches(Doyle et al., 2023).

Fig. 4 .
Fig. 4. Two-photon vision: differences in rod-and cone-stimulation ratio in comparison to one-photon vision.a) Dark adaptation curves after bleaching with white light (7.3•10 6 Td•s) obtained for testing the retina with a one-photon stimulus (520 nm, black circles) and a two-photon stimulus (1040 nm, 200 fs, 76 MHz, red circles).Stimuli were formed in a thin ring due to fast scanning.Data were adapted with permission from (Ruminski et al., 2019) © Optical Society of America.b) Mean pupillary light reflex (PLR) measured for 14 healthy volunteers for one-photon stimulation (blue and green solid lines: 520 nm, LED and laser, respectively) and two-photon stimulation (1040 nm, 200 fs, 76 MHz; red solid line).The brightness of each stimulus was matched for each subject individually in a separate procedure.Stimuli were fovea centered circles (LED) or spirals (fast scanning lasers) of 3.5-deg diameter.Figure from (Zielińska et al., 2019).

Fig. 7 .
Fig. 7. Two-photon microperimetry.a) Psychometric functions for one-and two-photon vision derived as logistics functions fitted to experimental data obtained for one healthy volunteer.The transition range for IR is equal to ± 1.1 dB, while for VIS it is ± 2.2 dB. Figure reprinted with permission from (Ruminski et al., 2019) © Optical Society of America.b) Bland-Altman repeatability plots for visual one-and two-photon sensitivities of 17 healthy volunteers measured with two-photon microperimetry, as described in (Ruminski et al., 2019).Figure reprinted with permission from (Ruminski et al., 2019) © Optical Society of America.c) The average IR sensitivity value as a function of age is shown for the normal population (blue crosses), compared with that of patients with cataract (green diamonds), AMD (red circles) and diabetic retinopathy (purple crosses).The solid and dashed lines refer to the 0.50 quantile of the normal and retinal-disease eyes, respectively.Figure reprinted from (Palczewska et al., 2023), with permission from Elsevier.d) Average maps (16 volunteers) of scotopic two-photon sensitivity are shown for the fs laser (1040 nm, 253 fs, 63 MHz) and the ps laser (1028 nm, 12.2 ps, 19 MHz).The error bars correspond to one standard deviation.The MPE level is indicated as the semi-transparent red plane at the bottom of the graph.Figure reprinted with permission from (Marzejon et al., 2023) © Optical Society of America.