: Usual DPI to PPI ratio I know that DPI (dots per inch) refers to actual printed dots per inch. And PPI (pixels per inch) refers to RGB pixels per inch. One printed RGB pixel is composed of

@Si6392903

In theory, the relationship is given by the amount of "grays" you need.
DA01 comented an aditional unit, the LPI wich makes things easier to explain.

DPI - LPI

I'll translate my images later, but here is an explanation:

A line is formed by groups of printer dots. In this image, 64 printer dots (8x8) form a Line dot. This way you can have a diferent size dot, to achive a diferent level of gray.

Let us think that we have this specs:
I. Printer at 1200dpi
II. Printing at 150 lpi

The mathematics are this: 1200/150=8. (on each dimension) 8x8 = 64. You can only have 64 levels of gray.



On a comercial offset film or plate you have at least 2400 dpi, so at 150 lpi you can have:

2400/150 = 16. 16x16= 256. You can have 256 levels of gray.

Laser printers

On a black and white printer you can see this in action. If you see bandages, this means that the printer is using a small matrix of dots, lets say 8x8 or 4x4.

LPI - PPI

The LPI - PPI ratio is recomended 1:2, so if you want 150 lpi you need 300 ppi. But this can be lowered to a 1:1.41 ratio, giving you 212 ppi.

Error difusion

Although the same rules for creating a single printed pixel on an error difusion printer (ink jet for example) can apply, where you need a 16x16 "zone" for each pixel, this relationship is really blurry, becouse you in reality have random dots. So, the ppi needed depends on the quality of the print (and viewing distance), rather than a DPI-PPI relation.

Edited answering your comment

A 2500 dpi printer, (asuming the resolution is the same horizontal and vertical) will give you a theorical dot of 10.16 microns.
1 inch = 25.4 mm
2500/25.4=.01016

If you want 256 lvls of color on that pixel you need 16x16 dots, so you need
10.16 x 16 = 162.56 microns.

In theory you could use a 100 color scale (10x10), which are cmyk values, but the truth is that thoose files are still 256 levels per channel.

So 2500/16 = 156 ppi (using error difusion and square pixels)

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@Shelley591

You're missing another key number: LPI. LPI is 'lines per inch' and refers to the number of 'lines' of dots that will be used to make up an image.

That can vary and depends more on the substrate being printed on than the source image. For instance, newsprint requires a very low LPI. High quality glossy paper can withstand a much higher LPI.

As such, there is no hard-and-fast translation between 'pixel' and 'number of printed dots'.

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@Vandalay110

If you can find a 600-1200 dpi sublimation dye printer, and if the continious tone it produces for you is colorfull enough then this would probably work out for you.

You can also go for chemical processing. Some photolabs still do this but in my locality it is usually limited to about 300 dpi which isn't good enough for 50 µm  which is your target.

Laser printers with 2400 - 4800 dpi could do something towards this kind of result. A 4800 dpi laser would have a 9X9 superpixel in a 50 µm2 that is probably a sufficient color resolution (especially with stochastic rastering). Whether or not it will stand to scrutiny at good level is another thing. A 4800 dpi inkjet with many intermediate colors and variable dot pich would probably do it better. But these would not be very good at microscopic zooms.

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