Magnification of a printed image

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Stanley
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Joined: Sun Aug 02, 2009 2:34 pm

Magnification of a printed image

Post by Stanley »

Hi everyone,

I took this closeup with my iPhone of a dead fern. The photograph has nothing special about it, but I wanted to understand what my magnification factor was.

I saved the picture and produced the annotation in Photoshop Elements, which automatically saved the image with a resolution of 28.346 pixels per centimeter (that is, 72 pixels per inch).

If you look at the picture of the fern next to the ruler, you can see that the fern measures just about 2.5 centimeters exactly. I used the ruler in Photoshop Elements and set it to measure in pixels, and the length of the fern in the Photoshop photograph was just about exactly 825 pixels. Thus, 825 pixels divided by 2.5 centimeters comes to 330 pixels per centimeter.

Now, when I produce a full-scale print of the image, the length of the fern measures 7.6 centimeters. Thus, 825 pixels divided by 7.6 centimeters comes to just about 109 pixels per centimeter.

Finally, therefore, let us divide 109 pixels by 28.346 pixels to get almost 3.85.

So here is my question, I guess. I have magnified the image by 3.85. Is that correct?

But then, let’s forget about pixels and just take the length of the fern in the printed photograph — 7.6 centimeters — and divide it by the actual length of the fern — 2.5 centimeters.

And here is what confuses me — 7.6 centimeters divided by 2.5 centimeters is 3.04, and this value is substantially less than 3.85.

So, what is my magnification factor?

Thank you.

Stanley

Image

ray_parkhurst
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Post by ray_parkhurst »

Your iphone probably has a 1/3" main sensor, which is approx 4.8x3.6mm. Could be smaller, depending on model. Which model do you have? Assuming 4.8x3.6mm, you calculate the magnification by dividing the sensor size by the measured field of view. Further assuming you did not crop the picture width, your horizontal field of view is ~7.3mm, so your magnification is 4.8/7.3=0.66.

rjlittlefield
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Re: Magnification of a printed image

Post by rjlittlefield »

Stanly, when thinking about magnification it is critical to be clear about one thing: "Magnification compared to what?"

The subject line of your post specifically asks about "Magnification of a printed image", and you've done the very smart thing of including a ruler when you took the shot.

So then it's simple to compute magnification of the print compared to real life. Just do what you said: take the length of the fern in the printed photograph — 7.6 centimeters — and divide it by the actual length of the fern — 2.5 centimeters. The result is 3.04X, as you calculated. The printed image of the fern is 3.04X compared to the fern itself.

All of the other numbers that you've calculated, the ones based on pixels, have their roots in other numbers that are pretty much arbitrary, irrelevant, and misleading. The number "72 pixels per inch" that comes out of Photoshop Elements is completely arbitrary and has nothing to do with the image content. You would get the same number whether you were taking a picture of a landscape or a poppyseed.
ray_parkhurst wrote:Your iphone probably has a 1/3" main sensor, which is approx 4.8x3.6mm. Could be smaller, depending on model. Which model do you have? Assuming 4.8x3.6mm, you calculate the magnification by dividing the sensor size by the measured field of view. Further assuming you did not crop the picture width, your horizontal field of view is ~7.3mm, so your magnification is 4.8/7.3=0.66.
I think Ray has slipped a decimal point. Your horizontal field of view is ~7.3 cm = 73 mm, so the calculation should go as 4.8/73 = 0.066 . But then that number is comparing the image of the fern on the sensor against the fern in real life. That number would be the "optical magnification" = 0.066X.

Optical magnification is often meaningful and has great interest to people in this forum who are in the business of mixing-and-matching lenses and sensors.

But to anybody who is mainly interested in the subject, optical magnification won't mean much and will probably give the wrong impression. The very same print could have been produced with a different camera at a far different optical magnification, say 0.5X on fullframe, but in the end it's the same fern and the same print.

--Rik

Stanley
Posts: 83
Joined: Sun Aug 02, 2009 2:34 pm

Post by Stanley »

Hi Rik and Ray,

Thank you very much for your responses.

Let me study what you wrote.

Stanley

ray_parkhurst
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Re: Magnification of a printed image

Post by ray_parkhurst »

rjlittlefield wrote: I think Ray has slipped a decimal point. Your horizontal field of view is ~7.3 cm = 73 mm, so the calculation should go as 4.8/73 = 0.066 . But then that number is comparing the image of the fern on the sensor against the fern in real life. That number would be the "optical magnification" = 0.066X.
--Rik
Oops...thanks for catching that.

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