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Study of the retinal image

The retinal image

The retina lining the inner wall of the eye, but it's the macula, at the posterior pole of the eyeball, which is the seat of the central vision. Within the macula, the so-called 'Foveal' retina is a fine vision, that is used to read a street sign, discern the foliage of a tree in the distance, read a text, etc. This area occupies only an area of a few square millimeters. It contains photosensitive cells called cones, which the collector surface is only a few microns square: these retinal "pixels" are for most purposes less than 2 microns wide (2 thousandths of a millimeter). The surrounding world is made up of light sources primitives (the Sun, the stars, a glow worm, a simple light bulb) and secondary (objects that reflect or passively transmit part of the light of the original sources). Light is made up of energetic particles without mass, called "photons": this a little ballistic description is not quite complete because some experiments show that light is also provided with wavelike properties.

Rather than address a debate on the nature of light, we will consider simply that the mission that falls to the eye is to collect a portion of light scattered by the source information, and to form an accurate picture, regardless of the nature of this information. In geometric optics, light rays can be understood as an abstract representation of the path of the photons emitted from a source; They especially predict where will form the sharpest image of an object "seen" by an optical system. Form a retinal image enough 'faithful' to a light source, to capture and then converge on the retina light rays that this source emits. To simplify our study, let's first find out that it is possible to assimilate, and whatever its complexity, the Visual pattern observed a set of basic structures. Then, we will look at the way in which the basic elements of the scene are "Graphic" on the retina.

The image as a set of basic points

For example, the most basic light source: the star. It is the simplest images whatsoever given to contemplate: due to its distance from the Earth, it appears as a bright point which stands a black and uniform background. Rays that the Sun emits in all directions, the eye of an earthling collects only an infinitesimal portion. They form the net of the star on the retina, focused image in terms of the photoreceptors, we conceive that these rays should meet there, IE has come across in a unique and located point in this plan.

image of a star by the eye
The star in the night sky is a basic picture: the emitted rays diverge from the star, in all directions of space. A part of these rays can be received by an observer who directs her eyes toward the star. Because of the huge distance from the star to the dimensions of l "eye, captured rays are considered to be parallel. The cornea and the lens must deflect (called "refraction") these rays to the retina, where its rays will have to "cross".

Captured rays must thus converge on a distance of the order of about 2 cm: this distance corresponds to the length of the eyeball, between the cornea at the front of the retina at the back. Yet the rays have diverged since their stellar source, which emitted the light in all directions of space. However, because of the astronomical distance from the star, which is located at years lights, the rays picked up by the eye are seen as Parallels because from a source "at Infinity". Their later convergence towards the retina is ensured by the effect that print the cornea and the lens to their journey.  The angle of deflection inflicted on the rays by these ocular structures must be adjusted with precision: If the rays meet too forward or back of this plan, they will form an image enlarged, which will then form a disk and not a point. This will affect the sharpness and contrast of the retinal image.

task of defocus
The retinal image of the star is puncture if the rays are focused in the retinal plan. She takes the appearance of a disk if the captured rays are not exactly focused in the retinal plan. This occurs when the eye is "too long" (myopia) or "too short" (hyperopia) with the focus of the eye distance.

When the rays are not focused in terms of the retina, they are called "defocalises": they impress the retina are forming a task of defocus: the dimensions of this task are superior to that of the point that form the rays to the place where they intersect)see for example: the vision of the myopic blur) At this point, it must digress and get away from the formality of geometrical optics, which equates the displacement of light to the path of rays. A one-time appearance object (the star) can produce a strictly one-time image, at the precise intersection of the rays: we call this property to make a point source an image point the «» stigma ». In reality, the light being fitted with wavelike properties, straight trajectories may not materialize all of the path that use light waves. In contact with obstacles, these waves are a phenomenon of «» diffraction ', which leads to a deviation of their trip; the waves spread a little after overcoming of the obstacle.

Diffraction and PSF
Eye and task d defocus light averaging

For the eye, everything happens as if the rays which were the edge of the iris (which delineates our pupil, the natural iris of the eye) see their slightly deflechi trip outside. It's iris pupille, "collector light admitted by the eye opening", and whose diameter is spontaneously modified to regulate the luminous flux received by the retina, which produces the phenomenon of diffraction. So captured light rays cannot be focused into a mathematical point, but at least form a circular task, whose dimensions depend on the pupil, and the wavelength of the light captured. Diffraction prevents the 'rigorous ': stigma This is not necessarily very harmful for vision, since the dimensions of the retinal photoreceptors (the "pixels" in the retina, that 'sampling' the retinal image) are either one-time or even infinitesimal.

Cones and retinal image
The image projected onto the retina is sampled by the photoreceptors of the fovea (the cones). The size of the cones (their density) determines the amount of detail that the retina can process, a bit like a screen will represent more details if it is more 'rich in pixels. The collecting area of the cones has roughly the same diameter as the task of illumination optimal that the eye can form on the retina (the image of a point source cannot be strictly punctual due to diffraction). The size of the cones determines the ability of sampling of the retinal image.

In reality, Nature has done things since the dimensions of the task of illumination of the retina that is formed from the observation of a point source are similar to those of the finest photoreceptors (minimum diameter is close to 1.5 to 2 microns). The size of the photoreceptors (which derives the density, that is to say the finesse of the paving of the surface of the retina) imposes an upper limit to the richness in details of the retinal image. To ensure that this limit is reached, must be the task of lighting not significantly wider than the collector surface of a photoreceptor)see the page devoted to Visual acuity and) density in photoreceptors) Looks and dimensions of this task of illumination play a role towards the Visual acuity and the optical quality of the human eye... So-called exploration technology "aberrometriques" allows the ophthalmologist to study: the issue task of illumination of observation of a basic source point (ex: a star) is called 'The point spread function' (EFF), or «» Point Spread Function"(PSF).   To understand the importance of the OGP on certain aspects of vision, consider not one, but two stars close together in the sky. Will there be eye required visual acuity allows to distinguish, that is to separate the retinal image of these two stars, yet very close together in the sky? To distinguish each of the stars bright, their retinal images, these focal tasks, should be disjoint, or at best not to encroach on the other.

retinal image separate sources
The retinal image of two nearby stars on the sky can lead to the vision of two separate stars if the retinal image of each star is projected with enough on the retina: the gap depends on the width of each of the tasks of illumination. A schedule condition is that the density in photoreceptors is sufficient to "sample" the respective images of stars.

 

images retinal hypermetropic eye
In this example (farsighted) 'too short' eye, the plan of the retina is located in front of the plan where close from the star couple rays intersect. The task of illumination of each star is a disk, and disk encroach on the other: the retina sees only a single point: the stars cannot be "separated."

Our vision used us that too rarely to observe and distinguish it from the stars in the beautiful summer skies. In everyday life, it is used to "see" much more complex patterns, to orient, identify obstacles, recognize familiar faces, read, watch a computer screen or TV, etc... These Visual tasks have in common the same prerequisites: form an image of the world surrounding enough faithful on the photosensitive retinal tissue. The case of the one star or two were relatively simple to understand; but that would be a pattern more complex as a landscape, a face? We can go back to the simple star case, considering a complex pattern like a set of basic sources pointslike painters of pointillist school representing the world as an assemblage of touches in the form of colored dots. Within a complex image, isolate one point elementary, at the center of the observed pattern. This point will become a reference. Its retinal image will stem from the capture of the rays it emits, and which will form after refraction by the cornea and the lens a spot light on the retina, which size and shape stem from the way in which these optical structures of the eye focus captured rays.

retinal image letter E
The letter 'E' is considered to be a set of source points elementary contiguous. We consider that the retinal image is the juxtaposition of the respective images of each elementary point.

The quality of the focus of this point stems from the combined effects of any optical imperfections (aberrations) and the inevitable diffraction. However, this quality is identical for all points close to our basic reference point. The image received by the Central retina at the level of the fovea, the seat of the fine vision, comes from the juxtaposition of the tasks of illumination of these adjacent points. This central invariance of the PSF can rebuild or simulate the retinal image of an intricate design, thanks to the simple retinal image of a point source.

retinal image of a point source elementary
Can be considered a complex image as a set of point source juxtaposed. The basic source point image will be a "task of retinal illuminance" necessarily less compact, due to diffraction and optical imperfections (called aberrations) considered eye. You can not really see the retinal image of an eye, but some techniques of exploration as the OPD to "predict" the way how the eye forms an image of an elementary point (one speaks of calculating the PSF). In this illustration, the basic source point is represented as a vertical line, whose height is proportional to the light intensity. The distribution of the energy of the image point has a profile inverted v, due to bright sprawl.

We have seen that the mathematical function that allows to describe the shape of the focal spot is called the point spread function (PSF: Point Spread Function). Its name is quite telling, because less will be sprawl, better will be the quality of the retinal image. The operation that allows to reconstruct the retinal image of a complex object by applying to each of its basic points spread suffered by the reference point is called the convolution.

convolution and simulation of the image retinienne
If one knows the PSF, we can predict the retinal image. The reference image is broken down into a set of contiguous elementary points. Each point is 'convoluted' with (undergoes sprawl of) the PSF (EFF = for the point spread function). When the point spread is important, the images of adjacent points encroach on the other: This explains the retinal image blur, and the inability to distinguish certain letters. The PSF of the sketched here eye could be a look nearsighted or farsighted. THEastigmatism causes asymmetrical spread of the task of illumination, which adopts an oval outline.

Like the first astronomers who scanned the night sky, believed there discern familiar motifs which they named constellations, it is very convenient for specialists of optics Visual to represent a scene as consisting of a constellation of point elementary light sources... This set is made of contiguous points, like those of a pointillist painting.  More Visual acuity, the more the eye can discern separate basic points within an intricate design, and enrich the perception of the details of the observed scene.

The image as a network of spatial frequencies

There is another way to see the light objects of the surrounding world, which, although it provides a powerful way to study for the study of certain characteristics of human vision, we appear less intuitive. A musical agreement is similar to the superposition of different sound frequencies, which each frequency determines the pitch of the note she wears, and the amplitude intensity (i.e. the volume it occupies within the agreement). By analogy, any Visual pattern can be likened to a superposition of «» spatial frequencies ». These are theoretical constructions, but their scope is broad: any Visual pattern can be decomposed into a clean set of spatial frequencies. This field of study is not part of geometrical optics, and the next paragraph can be skipped by the eager reader. It is however interesting to continue our foray into the field of the spatial frequencies to better understand the methods of analysis of quality and image processing. The spatial frequencies are "undulating fringes": their brightness alternates continuously and regularly between lighter and darker areas. The retinal image quality does not depend on that the density of the collected details; It also depends on the return of a good contrast. The rendering of the contrast is the ability to discern not just two stars close in the night sky when they shine in a comparable way (separate colon white on a black background), but to continue to do so when their brilliance turned pale, while the sky cleared him (it would be now to separate two gray points clear on a dark grey background).

spatial frequencies and letter E
By a somewhat bold musical analogy, we can assimilate these spatial frequencies to the main 'notes', those who dominate in agreement 'E '. So that the eye can perceive the letter 'E', it is important that the contrast of these frequencies (the intensity of the main notes) within the retinal image is non-zero, and greater than the minimum threshold of perception of contrast. To encode for e such as depicted here, with sharp edges, use other frequencies space, "highest". If all of these frequencies is transmitted with a contrast to the retinal level, the letter will be identifiable and perceived as NET. If some of the higher frequencies is transmitted with sufficient contrast to be detected, the eye will be able to identify the presence of a letter "E", provided that at least the frequencies shown in this illustration are transmitted with sufficient contrast.

A spatial frequency is a variation of intensity profile, which undulates like a sine wave, alternating darker areas (of the gray to black - minimum - before returning to the medium grey) and brigher areas (of the gray to white - maximum - before returning to middle gray). The combination of a dark area and a clear zone constitutes one cycle: the number of cycles per unit distance sets the value of the spatial frequency. The higher the frequency, the more mnay the cycles. We understand intuitively that the degree of a frequency is proportional to the fineness of detail that she 'codes' in the picture. Its amplitude (maximum if a cycle goes from white to black, less if a cycle is from light gray to dark gray, zero if the gray level does not change) corresponds to contrast that has such frequency in the image. We have seen that like in a musical chord which consists of several music notes, any picture could be understood as the superposition of a set of superimposed spatial frequencies. This property does not only apply that to the observed pattern... it's also about the retinal image! In addition, the image of a spatial frequency by an optical system is that same spatial frequency (same number of cycles per degree), but whose the contrast is modulated (always on the downside, not because of diffraction).  The contrast of the image space retinienne frequency modulation 50 pcIf its composition in spatial frequency is identical to that of the observed pattern, and their amplitude is little diminished, the picture will be faithful to the original. Of course, because some of the light emitted and captured by the eye diffracted at the edges of the pupil level, frequency composition of the retinal image is always a little less "rich" than that of the Visual pattern of reference. The loss of detail in an image (the blur), is due to excessive reduction of the contrast of the high spatial frequencies in the retinal image. these frequencies, which encode for the details of the image, is no longer seen. A blurred image is impoverished in details, this is a picture where we have removed some spatial frequencies.

modulated under the threshold contrast
The contrast of the object (a spatial frequency) is 100%: due to diffraction and any optical aberrations, the contrast of the frequency space image is reduced: this contrast can be below a threshold below which Visual channels cannot transmit information. The frequency is "cut off", and the details that they encode in the image are no longer perceived.

At the end of a calculation which will silent the complexity, we can record called "modulation transfer curve")FTM or MTF in English) which reflected how the eye modulates the amplitude (the contrast) of each spatial frequency. The position of the points of the MTF curve is a little similar to what would be the audio mixer sliders: they translate the modulation of the contrast that undergoes frequency (more or less severe, medium, acute audio more or less low, medium or high in optics).

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