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Visual acuity: screens, concrete examples

Visual acuity: what details can I collect?

This page is dedicated to the study of the relationship between Visual acuity and ability to distinguish details, through concrete examples (the digital screens, urban billboards, etc.) and applications in everyday life. To become familiar with some basic concepts, it is advisable to consult the page dedicated to l "Visual acuity, that is the ability to solve constituent details of the images.

The Visual acuity of the human eye partly determines the resolution of digital screens, the dimensions of public billboards and that of their inscriptions, etc. Indeed, to be realistic, and "nice" to the eye, the "frame" of a screenshot (the lines of points - pixels - that constitute) must remain 'invisible '. In other words, the resolution of the image displayed or projected to exceed the maximum resolution the eye (we speak of 'under sampling").

 

Visual acuity and screens

The screens have invaded our space and time spent watching these 'digital windows' of growing... (as evidenced by may be visiting this site!)

Screen TV / LCD

Modern screens are made up of LCD matrices: says "HD" (high definition) display consists of a matrix of 1920 points by lines x 1080 lines: either slightly more than 2 million points or 'pixels' across the TV screen (standard display of television was before 1024 × 768, or a little less than 800 000 points). The pixels are even composed of a mosaic of 'subpixels' basic (red, green, and blue), which the arrangement varies according to the designs and technology (LED or AMOLED). Approached sufficiently near a LCD of standard size slab (ex: TV screen), we can easily distinguish these pixels, or even the under pixels that compose. Within 2 metres of a slab LCD 46 inch full HD (1920 x 1080 is 47.9 pixels per inch), an eye has 10/10 Visual acuity can distinguish the pixels. It is preferable to look at the screen at a greater distance.

The resolution of a screen is not the only parameter to take into account to assess the quality of an image: the contrast, the refresh rate of the images, Colorimetry, are so many other variables to consider. This page is limited to exploring the relationship between Visual acuity and perception of the basic details of a static image.

The following figure to establish some basic reminders to understand what follows. The main difficulty in this context is to understand the meaning of the units used to describe the resolving power of the human eye.

representation of the correspondence between cycles per degree and acuity

The resolution power of the eye is traditionally expressed in tenths (e. g. acuity of 3/10), or, more technically, in numbers of solved cycles per degree. It is always a question of quantifying the number of "details" that the eye can distinguish when they are inscribed in an angular sector, or the size of the minimum angle at which the finest details can be inscribed. The minimum resolution angle in this example is equal to 1 minute of arc, in which a half cycle is included. Remember that 1 minute of arc is equivalent to 1/60th of a degree. It is therefore possible to solve 30 cycles in one degree for a visual acuity of 10/10 (solving means distinguishing two black lines or two white lines as separate, which requires distinguishing or sampling the intermediate line of the opposite colour. The maximum visual acuity of the human eye, in terms of separating power, can reach 20/10, or 60 cycles per degree: the sampling limit of the retina is reached: the features of the cycle, black or white, are each "projected" onto adjacent retinal cones. If the lines correspond to screen "pixels", then the screen resolution can be considered to be "equivalent" to the "sampling power of the eye considered. Under the same observation conditions, increasing the screen resolution (reducing the size of the pixels) no longer offers the eye looking at it the possibility of "seeing" the pixels (the eye "under sample").

 

 

 

About calculations in Visual acuity and the spatial resolution of the observed patterns, it is preferable to use the expression in cycles per degree than in «»  "or fraction. It should also be recalled a few useful equivalences: a Visual acuity of 10/10 corresponds to solve 30 cycles enrolled in one Visual angle 1 minute of arc. A cycle consists at a minimum of a couple of points (or pixels): 1 dark, 1 light. Them spatial frequencies which are constituent repetitive patterns of images are expressed in number of cycles per degree.

Knowing thata human eye has a maximum resolution close to 60 cycles per degree (20/10: maximum sampling of the retina when the eye is perfectly corrected). What spatial density of "pixels" is required to display an image 'smooth' (without visible frame), at a screen size given, observed at a distance? "Required" density means "exceeding" the resolution of the eye, so that it can distinguish the lines or the constituent fabric of the image displayed on the screen (we remind that the eye can resolve in a given angle constituted grounds for a number of light and dark lines alternating, a pair of lines = 1 claire + 1 dark setting a cycle).

To simplify the calculations, we will choose a value of 50 cycles per degree for power maximum resolution of the considered eye (which corresponds to Visual acuity decimal 16.5 tenths, the theoretical maximum visual acuity of the human eye is 60 cycles per degree is 20 tenths). We will thus place in a senior event, most of the texts on the topic choose a Visual acuity of 10/10 as resolution threshold.

This eye is Emmetropic of course (it's or short-sighted, longsighted, astigmatic or so perfectly corrected these defects), and accommodates enough in near vision (no presbyopia).

For example, a 16: 9 TV screen high resolution - full HD (1920 × 1080 definition), 46 inches diagonal, or 117 cm (about 47 pixels per inch - DPI, one inch is equal to 2.54 cm). The height of this screen is 57 cm and width of 101 cm. It should be noted that for a definition, the resolution of the screen decreases with the size of its diagonal, and only need to move back if it does not feel a drop of the resolution of the screen.

If the screen is observed at a distance of 3 metres, the angle it forms with the eye height is

2 x Inv (Tan) (0,285/3) ≈0, 188 rad = 10 °

Visual acuity and screen full HD resolution

A 46-inch screen seen at a distance of 3 metres, an angle of 10 ° in height with the eye. If the eye has a maximum resolution of 50 cycles per degree, it can distinguish 500 cycles registered in this key sector, which requires 1000 pixels, or a little less than what offers the native resolution of the display.

If the maximum resolution of the considered eye is 50 cycles per degree, an angle of 10 ° from the eye embraces 10 x 50 = 500 cycles. As it takes two pixels to form a cycle (Nyquist rule), it must be that there is at least 1000 pixels in these 10 ° (or 100 pixels per degree). The screen being 1080 pixels resolution, she slightly exceeds that of the eye, which is not likely to see the constituent lines of the image.

Under the same conditions of observation, a screen older generation equipped of 768 lines (768 pixels for a column) would however "on sampled" by eye, with a risk to perceive horizontal 'frames'.

A new generation of TV screen to "ultra high definition" has recently emerged: the definition of these screens in pixels is doubled towards HD slabs, and 3840 × 2160 pixels (format: 1.78: 1) is 8 294 400 pixels. They allow in theory to quadruple the surface of the screen without loss of resolution of the observed image (if the eye is located at twice the distance of a HD screen). With such a screen, we need to analyze less than 1.50 m of a slab of 46 inches to 'sur-échantillonner' the picture displayed ('see the lines' of the screen). The resolution known as "4K". is about the same (4096 × 2160 pixels) than the "ultra high definition" resolution, but fully used by cinema or home theater projectors, it will display details that the resolution far exceeds that of the human eye, unless you get really close to screen (or projected on a very large screen).

In General, remembered for a screen size and distance of observation data to a minimum threshold of "100 pixels per degree" to avoid a "oversampling" by the eye.

 Digital tablet screen

An example of a digital Tablet mini iPad (version 2 or 3) with his famous "Rétina" display Displays a definition of 2 048 x 1 536 pixels (themselves composed of subpixels), and the screen diagonal is equivalent to a density of 326 pixels per inch (DPI), or 13.3 pixels per mm. When you hold the iPad at 25 cm from the eye, this resolution corresponds to register a cycle in 0.0003 radians, or 0.017 degree, or even 58 cycles in a degree which corresponds to a resolution equivalent to the maximum sample capacity of the retina.

THEair iPad (not mini) is fitted with an equivalent definition, 2 048 x 1 536 pixels, but the larger size of the diagonal (9.7 vs 7.9 inches) results in a density of 264 pixels per inch (DPI) or 10.8 pixels per mm. 25 cm, the screen offers a resolution whose spatial density is 47 cycles per degree, less than the retinal resolution. To match this, observe the screen of the iPad at a distance a little more large 33 cm.

Smartphone screen

The definition of the screen of theiPhone has continued to increase over the generations. The one of theiPhone 4 was 640 x 940 pixels, one of theiPhone 5 of 640 x 1136, that of the iPhone X of 2,436 x 1,125... but the screen is also a little longer at each generation: the spatial density in pixels (resolution) is thus almost identical for both generations of iPhone 4 and 5. Things get a little more complicated with the iPhone 6 and 6S, two models with different screen sizes, resolution and also different. The pixel density has significantly increased with iPhone X:

The native definition of the screen of theiPhone 5 East of 1136 x 640 pixels, or a density of 326 DPI, or 13.3 pixels per mm. This resolution is equivalent to 58 cycles per degree, to 25 cm.

This resolution is close to the maximum resolution of retinal, and certainly warrants 'retina display' name, for an observation to 25 cm. In the past, the apparent size of the screen reducing, even less, the eye can resolve a still higher apparent resolution.

For an observation to 25 cm, density of 330 pixels per inch is enough to exceed the resolving power of the eye (assumed well developed for this distance of 25 cm; this distance requires a strong accommodation or wearing glasses for reading).

The iphone 6 is available in two versions:

The screen diagonal measures 4.7 inches for theiPhone 6with a definition 1334 × 780, is 326 pixels per inch (DPI), or 13.3 pixels per mm.

THEiPhone 6 «more» He has a 5.5 inch screen whose definition is 1920 × 1020, or 401 pixels per inch (DPI), or 16.4 pixels per mm. The screen of this model is bigger and also more dense in pixels.

For the screen of the iPhone 6 standard, angle allowing to register a pixel is equal to 1/13.3/250 = 0, 0003 radians = 0.017 degree, which is an angular resolution of 58 cycles per degree... Almost the maximum retinal resolution, estimated close to 60 cycles per degree. This resolution obviously exceeds the 'classic' of the human eye of 10/10 resolution (30 cycles per degree).

In its version 'more', the same calculation from a resolution of 16.4 pixels per mm provides an angular resolution of 71.5 cycles per degree, which exceeds the retinal resolution (for a comment to 25 cm).

THEiPhone Xwith a resolution of 458 pixels per inch, is almost over-equipped with retinal resolution capability for observation at a standard reading distance.

The screen of the Galaxy S3 had a definition a little higher than that of the iPhone 5 (1280 x 720) but this form being larger (+ 18%), the spatial density in pixels is substantially the same as that of this model. The next generation, the S4 Galaxy, offers a definition of 1920 by 1080 pixels ('full HD'), with a density of 441 pixels per inch, or 18 pixels per mm, and 78 cycles per degree. The Galaxy S5 offers the same definition, a slightly larger screen, and a density of 423.64 pixels per inch (pop) or 17.3 pixels per mm and 75 cycles per degree. The  Galaxy S7 has raised the bar even higher, with a density of 577 pixels per inch, and this density has been repeated for the Galaxy S8.

The Galaxy Note 4 offered one of the highest resolution on this type of device, referred to as "phablette" due to the size of its screen to its release (hybrid phone / Tablet): despite the significantly larger surface of the display, the definition reached 2560 × 1440 and resolution 518 pixels per inch, or... 92 cycles per degree, once and a half the retinal maximum resolution, always for a comment to 25 cm. We can calculate that it Note 4 should be approached about 16 cm from the eye so that the theoretical retinal sampling exceeds the native resolution of the screen. This presupposes the absence of presbyopia, and a good power of accommodation (or a myopia close to 6 Diopters, which will then allow to observe the screen comfortably at this distance without accommodation). This high-density display requires special arrangements of the sub-pixel matrix ("diamond pentile" display). This matrix has more green sub-pixels (518 dpi) than red and blue (366 dpi), for a total of 7.3 million sub-pixels! Note 4 could be used as a display screen, inserted into the Samsung Gear VR virtual reality headset. Observed at a shorter distance and with the magnification of the eyepieces, this resolution then became lower than the retinal resolution. For comparison, the Galaxy Note 3 screen had a 1920 x 1080 resolution of 386 dpi. This screen equipped the Virtual reality caseque Oculus Rift DK2 version.

under the rating 4 display pixels

The AMOLED matrix of the Galaxy Note 4 display was one of the densest in pixels of the phablets available in the early 2010's. The predominance of green sub-pixels reflects the increased retinal sensitivity for green.

It is legitimate to question the value of such a display density; observed at more than 16 cm, Note 4 theoretically offers the possibility of displaying display details that the human eye cannot see... However, the use of this display density is quite useful when Note 4 is placed in a virtual reality headset such as the Samsung Gear VR (for Virtual Reality), where its screen serves as a display system, and is observed behind a magnifying stereoscopic eyepiece system. The Galaxy Note 3 screen was used for thecaseque Oculus Rift (version DK2) display.

The Galaxy Note 7  did not represent an increase in screen resolution, with a pixel density of 506 pixels per inch (dpi), slightly lower than that of Galaxy Note 4 and later (Note 5): 518 dpi.

The Galaxy Note 8 offers a 6.3-inch screen with a resolution of 3840 x 2160 pixels for a comparable density: 522 dpi. This density is sufficient to exceed the retinal resolution for standard observation, but not for a virtuele reality headset due to the apparent magnification of the screen.

 

'Virtual' screen of Google glass

Despite the termination of the program Google glass in its original form, it is interesting to measure the resolution of this particular screen, which was "planned" in the field of vision of the right eye of the wearer by pico-projector with Google gogglesIt appears as a 15 inch screen in 16: 9 format that would observe one to 1.5 metres approximately. The apparent angle of the width (side vertical to the screen, with the virtual height of 32 cm) can be estimated at 12 °. For an eye with the maximum resolving power of 30 cycles per degree (Visual acuity 10/10), the number of pixels required for not "sur-échantillonner" the image (IE see pixels) is close to 360... However, the native definition of the Google glass screen is 360 x 640. It is more than likely that the choice of this definition and the apparent size of the screen is not the result of chance, but a compromise between display density and minimum performance of acuity of the human eye. Based on these calculations, a higher Visual acuity (ex: 50 cycles per degree - 16.5 tenths) may cause the perception of a 'frame' or the pixels on the virtual screen.

 

The perception of 'pixels' of a screen is the prerogative of the powerful eyes. Some displays are designed to be read by less powerful eyes. We leave here the field of "pixels" to focus the «details» to identify a picture (letter, motif, etc.).

Urban display

In this context, the dimensions of the panels and display are intended to be identifiable at great distance (up to tens of meters).

Name of streets

The Parisian panels (street signs) display letters whose height is close to 10 cm. Observed at a distance of 10 meters, a letter is part of an angle of about 0.57 °. The letter E is 2 cycles and a half (5 bars in total), or 4.4 cycles per degree: to be resolved, this letter requires a Visual acuity of 4/30 = about 1.5 tenths. Observed at 60 meters, Visual acuity needed to solve this letter and read the name on a street sign is almost 10/10.

The calculation of Visual acuity minimum to read street signs can also be done in the following way: the letter 'E' consists of 3 horizontal lines and a vertical bar. Horizontal lines have a width of 2 cm approximately (each line is spaced an interval whose width is also 2 cm). To read the name of a street, the eye must resolve details with dimensions of the order of 2 cm. Theoretical Visual acuity needed to read a street sign, of course, depends on the distance between the observer and this one.

The following figure represents the dimensions involved in the calculation of Visual acuity needed to read a street sign:

Visual acuity and Panel

The Panel includes letters whose details are about 2 cm. Visual acuity necessary for recognition of the Panel is a function of the viewing distance (minimum resolution angle calculation / MAR)

The calculation shown in the illustration (the small angle by the arcsine function approximation) suggests that a minimum Visual acuity of 1/10 (minimum resolution of 10 minutes of arc angle) is enough to read a street sign at 7 meters. On the other hand, few pedestrians we drivers could read a sign at a distance of 70 metres, despite a Visual acuity of 10/10: this is the reduction of contrast, the relative turbidity of the air to such a distance, etc.

Metro stations

Constituent letters to present views on the docks of metro stations in Paris are close about 1 m high. The width of the docks is about 4 meters, for a total width of 14 meters Gallery. Observed in 6 meters, a constituent letter in the display is part of 9.5 degrees with the eye.

view metro and required for a sufficient Visual acuity criteria

If the letter 'E' measure 1 meter high, each "horizontal bar" that constitute measures 20 cm. A clear bar and an adjacent cavity form a cycle. 6 meters, all of the letter is part of 9.5 degrees about, and there are so 2.5/9.5 = 0.26 cycles per degree.

The letter E represents 2 cycles and a half, or 2.5/9.5 = 0.26 cycle by degree angle. Expressed in decimal acuity, Visual acuity minimum to resolve this display is 0.26/30 = 0,009 ≈ 0.1 tenths (or 1/100th).

Observed from the end of the pier on the other side (at about 14 m), this same letter E fit in a 4 ° angle, and read the name of the station would then require an acuity of about 0.2 tenths.

 

Conclusion

This page offers a brief overview of the method of calculating "gauge" the resolving power of the eye to digital screens and the main signals encountered in urban areas. The ability of a pattern to be resolved depends on the spatial density of the details it contains, and of course, this calculation must take into account the viewing distance.

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