# How large is “one pixel” for S5 AMOLED display?

Referring to Samsung Galaxy S5 OLED Pixel structure in oled-display.net, in particular this image illustrates the S5 AMOLED pixels: To my understanding, the yellow rectangle should represent "one pixel" as it is the smallest repeating pattern.

However, doing a few maths:

118 micrometers = 0.00464566929 inches
1/0.00464566929 = 215.25423735 pixel-per-inch (ppi)


Which is very different from the announced figure: 432 ppi.

However, surprisingly:

215.25423735 x2 = 430.5084747 ~ 432 ppi


In another words, 432 ppi is concluded by seeing 1/4 of the yellow rectangle (59µm x 59µm) as "one-pixel", isn't it?

But why? In the 59µm x 59µm square, it contains only either Blue or Red. In simple words, repeating the 59µm x 59µm square cannot produce this pattern, isn't it?

• Didn't it happens they count green 'pixels'? For photo camera sensors it is common that twice the actual resolution is stated (single colour cells are counted instead of full RGB arrangement). – Vovanium Aug 5 '14 at 11:52
• On the picture yellow square outline two RGB pixels (red and blue outline one pixel), so actual resolution should be sqrt(2) times higher, approx 304 ppi. – Vovanium Aug 5 '14 at 11:57
• @Vovanium Thanks for comment. If colour cells are counted, original RGB sensors/displays could state their devices at 3x the actual pixels?? This is awful. I do agree with you that the red/blue square is one pixel, as they are self-repeating unit, and are able to represent any colours in the image, e.g. RGB(255, 0, 0). As the red/blue square is half the area of the yellow one, i guess that's why the ppi is doubled. (i will do the calculations later) – midnite Aug 5 '14 at 12:25
• For doubled ppi to be true yellow square should contain four cells (2×2). – Vovanium Aug 5 '14 at 12:31
• What if counting it at 45 degree incline? ... oops, seems not, neither. – midnite Aug 5 '14 at 13:19

I was about to file a query to Samsung Support. To ask better questions, I re-study the webpage again, and I came across this post having the table below: In the row of "Sub-Pixels Per Inch", we can see that only green pixels are having 432 ppi. Both red and blue pixels are at only 305 ppi.

Doing a few maths:

$$Closest\ (inclined)\ distance\ between\ red\ pixels = \sqrt{(118µm/2)^2 + (118µm/2)^2} = 83.439 µm$$ $$83.439 µm = 0.00328498426 inches$$ $$PPI_{red} = PPI_{blue} = \frac{1}{0.00328498426 inches} = 304.415 ppi \approx 305 ppi$$

This table verifies our PPI calculations and definition. According to these figures, pixel distance that is used to calculate the PPI should have been defined as the closest distance between two dots of the same colour, which can be independently turned on and off.

Is Samsung being tricky? Not exactly.

When I do more researches on S5, so as S4 as they have similar diagonal PenTile RGBG matrix (same pattern, different size and sub-pixel shape only, see the webpage), I got this from wiki:

PenTile RGBG layout used in AMOLED and Plasma displays uses green pixels interleaved with alternating red and blue pixels. The human eye is most sensitive to green, especially for high resolution luminance information. The green subpixels are mapped to input pixels on a one to one basis. The red and blue subpixels are subsampled, reconstructing the chroma signal at a lower resolution. The luminance signal is processed using adaptive subpixel rendering filters to optimize reconstruction of high spatial frequencies from the input image, wherein the green subpixels provides the majority of the reconstruction. The red and blue subpixels are capable of reconstructing the horizontal and vertical spatial frequencies, but not the highest of the diagonal. Diagonal high spatial frequency information in the red and blue channels of the input image are transferred to the green subpixels for image reconstruction. Thus the RG-BG scheme creates a color display with one third fewer subpixels than a traditional RGB-RGB scheme but with the same measured luminance display resolution. This is similar to the Bayer filter commonly used in digital cameras.

So, we have a few conclusions:

• The structure and dimensions in the oled-display.net news (it means the image in the question) are correct.

• Yes. S5 AMOLED display does having less than 432 ppi if we focus on red or blue sub-pixels. (They are of 305 ppi only.)

• However, according to wiki, the perception of resolution depends mainly on the green sub-pixels. So it is having 432 ppi on real-life images. (I believe for pure red and/or blue images, it has only 305 ppi diagonally.)

• Digital images are displayed at 432 ppi, as they are mapped to the green sub-pixels on a 1-to-1 basis. The red and blue sub-pixels are complements.

A side note:

In the last sentence in wiki mentioned our familiar cameras' Bayer filter. After re-studying again:

The raw output of Bayer-filter cameras is referred to as a Bayer pattern image. Since each pixel is filtered to record only one of three colors, the data from each pixel cannot fully specify each of the red, green, and blue values on its own. To obtain a full-color image, various demosaicing algorithms can be used to interpolate a set of complete red, green, and blue values for each pixel. These algorithms make use of the surrounding pixels of the corresponding colors to estimate the values for a particular pixel.

which means the image below is a 8 x 8 pixel sensor (instead of a 4 x 4 or else). That's because you are using the wrong formula. Have a look here.

First let's calculate the screen diagonal resolution (in pixel): $$d_p = \sqrt{w_p^2 + h_p^2}=\sqrt{1080^2+1920^2}=2202.91$$

Then PPI can be calculated: $$PPI = \frac{d_p}{d_i}=\frac{2202.91}{5.1}=431.9\approx432$$

Where:

• $d_p$ is the diagonal resolution in pixels
• $w_p$ is the width resolution in pixels
• $h_p$ is the height resolution in pixels
• $d_i$ is the diagonal size in inches (the number advertised as the size of the display)
• Hmm... I understand your formulas. You are using 1080 x 1920 pixels over a 5.1 inch monitor. However, if the image above describes the S5 display correctly, 1 pixel of size 118 micrometers = 0.00464566929 inches. For a 1080 x 1920 pixels screen, it will be 5.017 x 8.920 inches! Having its diagonal of 10.234 inches, it doubles the S5 screen! Thanks for answer. – midnite Aug 5 '14 at 10:31
• The problem is that your definition of pixel does not correspond to the one used when calculating PPI. You just take the unit cell width and call it a pixel... That might be good from your point of view but the widely used definition is the one I posted. – Vladimir Cravero Aug 5 '14 at 10:40
• Thanks for comment. But the number you used in the calculations are based on the resolution announced, i.e. 1080 x 1920 pixel counts. What is the definition of one pixel? To my understanding, it is either a repeating unit, or a unit that can represent a colour in the image, e.g. RGB(255, 0, 0). Let's say 1/4 of the yellow square does mean one pixel. The upper left and the lower right cannot display pure red, RGB(255, 0, 0). – midnite Aug 5 '14 at 12:16
• Well, I'd say that your definition of pixel is good. It's just not what they mean when they speak of PPI... – Vladimir Cravero Aug 5 '14 at 13:35