Does size matter?

[BearSummer]

I thought it would be fun to know how many mega pixels you actually need. So I did a little research and found the following pieces of information

1, The correct distance to view an image from is the same as the diagonal of the image.

2, The working definition of 20:20 vision is “the ability to resolve a spatial pattern separated by a visual angle of one minute of arc” which translates to 1/60th of a degree.

Time to do some math using rule #1….all distances will be in millimetres unless otherwise stated

A sheet of A4 is 297x210 so the correct viewing distance is (297^2 + 210^2)^.5 = 364mm (14.3 inches)

Doing the same with the other standard paper sizes

A4 viewing distance 363mm (14.3”)
A3 viewing distance 514mm (20.25”)
A2 viewing distance 727mm (28.6”)
A1 Viewing distance 1029mm (40.5”)

How much can we see at these distances. For this we need to use rule #2

The smallest detail we can see with 20:20 vision is one minute of arc or 1/60th of a degree, so how big is that at those distances.

If we position ourselves at the right distance to the print then a line drawn from our eye that hits the image at a right angle, with half a minute of arc above the line and half a minute of arc below the line. Time for some trig, we know the angle and the distance ...

1, tan(angle) = opposite/ajacent
2, tan (1/120th of a degree)=half height of detail/viewing distance
3, viewing distance x tan (1/120)=half height of detail

So lets solve for the above viewing distances

A4 = 363 x 0.000145444 x 2 = height of detail = 0.1058mm
A3 = 514 x 0.000145444 x 2 = height of detail = 0.1496mm
A2 = 727 x 0.000145444 x 2 = height of detail = 0.2116mm
A1 = 1029 x 0.000145444 x 2 = height of detail = 0.2993mm

If we convert these to pixels per inch (25.4mm=1 inch) then the following resolutions come out

A4 = 25.4 / 0.1058 = 240ppi
A3 = 25.4 / 0.1496 = 170ppi
A2 = 25.4 / 0.2116 = 120ppi
A1 = 25.4 / 0.2993 = 84ppi

Now we get to the fun bit, if you are a partner of a photographer or someone who wants a multi mega pixel camera then look away now.

How many megapixels do you need to fill the different sized sheets.

A4 = ( 297 / 0.1058 ) x ( 210 / 0.1058 ) = 5,571,012 = 5.6Mp
A3 = ( 420 / 0.1496 ) x ( 297 / 0.1496 ) = 5,571,012 = 5.6Mp
A2 = ( 594 / 0.2116 ) x ( 420 / 0.2116 ) = 5,571,012 = 5.6Mp
A1 = ( 840 / 0.2993 ) x ( 594 / 0.2993 ) = 5,571,012 = 5.6Mp

You may draw your own conclusions.

BearSummer

[deadpass]

That sounds about right from other things I've heard. However the bigger the sensor the more you can crop and still stay at or above the 5.6mp. Good info and math to back it up!

[S.Horton]

I am, therefore I crop.

;}

[BearSummer]

The other interesting thing is that once we know the resolution images are scalable, for example,

You want to create a 10x8, you know the resolution is 240ppi, so the image you need to crop to is 2400x1920 (4.6mp) and thats the same size for 16x10, 20x16, 32x20 so long as you view it from the right distance (because the resolution drops the further back you stand). If however you are going to stick your nose into the frame...

which is handy as im printing my 6Mp D60 to A3.

BearSummer

[BearSummer]

with the other paper sizes, all sizes in inches

10x8 viewing distance 12.8"
16x10 viewing distance 18.9"
20x16 viewing distance 25.6"
32x20 Viewing distance 37.7"

<snip>. Time for some trig, we know the angle and the distance ...

1, tan(angle) = opposite/ajacent
2, tan (1/120th of a degree)=half height of detail/viewing distance
3, viewing distance x tan (1/120)=half height of detail

So lets solve for the above viewing distances

10x8 = 12.8 x 0.000145444 x 2 = height of detail = 0.003725"
16x10 = 18.9 x 0.000145444 x 2 = height of detail = 0.005488"
20x16 = 25.6 x 0.000145444 x 2 = height of detail = 0.00745"
32x20 = 37.7 x 0.000145444 x 2 = height of detail = 0.010977"

If we convert these to pixels per inch

10x8 = 1 / 0.003725" = 268 ppi
16x10 = 1 / 0.005488" =182 ppi
20x16 = 1 / 0.00745" = 134 ppi
32x20 = 1 / 0.010977" = 91 ppi

<snip>look away now.

How many megapixels do you need to fill the different sized sheets.

10x8 = 10x268 x 8x268 = 5.8mp
16x10 = 26x182 x 10x182 = 5.3mp
20x16 = 20x134 x 16x134 = 5.8mp
32x20 = 32x91 x 20x91 = 5.3mp

[Jon]

Are you testing the accuracy of those numbers with that tiny font? How about using a readable size?

[Jim G]

I wouldn't be all that surprised - of course, it's always nice to be able to view it closer and have it still be sharp but I've printed 8mp 20x30" and it looks brilliant... the more the merrier, of course, but I'm not going to break the bank trying to get that 12mp or 21mp camera :)

[20droger]

Your math is correct, but some of your assumptions are suspect, and one important variable is missing.

The missing variable is the printer resolution. Printing the image inthe wrong number of dots per inch cam decrease image claity by clashing with the number of pixels per inch. (Can you say "moiré"?)

Also, one of your primary assumptions is that the viewer will view the image from the proper distance. This is almost never true. Few people do this, so a worst-case scenario should be used.

Anoth assumption is that the viewer has 20/20 vision. 20/20 vision is the vision of Joe Average, a completely mythical person. Almost no-one has truly 20/20 vision, eye tests notwithstanding, as they are only about 20% accurate, which is good enough for prescribing glasses.

In fact, the populace is becoming slightly nearsighted overall, do to the preponderance of close work being done daily. (Can you say "computer screen"?)

Age doesn't help.

The largest size image to be reproduced from a given number of pixels has been calculated many time, and is found in most camera manuals and books on digital photography.

You are right in that fewer pixels are needed that most people realize, however.