Help - pixels per inch paradox

In summary, the problem is that the number of pixels per inch cannot be calculated with the information given.
  • #1
aneikei
16
0
Hello, I could some help. I've reached some sort of paradox. Ultimately I'm trying to calculate the number of pixels per inch, given a pixel size of 5177 nm and extended at a distance of .7inch (.0178 meters)

(A) (60 arcsecs * 0.0178 meters)/206268 = 5177nm pixel per arcmin

(B) 5177 * 60 = 310,620 nm per degree.

(C) tan(55)*.7 = 1 inch (thus 55 degrees = 1 inch)

(D) 310,620 * 55 = 17,084,100 nm per inch

(E) 17,084,100 nm /5177 nm = 3300ppi

However, 5177 nm = .000204 inch
and 1 inch / .000204 = 4901

Thus, 4901 x 5177nm = 25,377,450 nm per inch
25,377,450 nm /5177 nm = 4901 ppi
which is way different from 17,084,100 nm per inch
17,084,100 nm / 5177 nm = 3300 ppi

What did I do wrong? Which is correct? Thank you in advance
 
Physics news on Phys.org
  • #2
I can not follow what you are trying to do. If there is a lens involved with focal lengths and other parameters, please supply some more detail.
 
  • #3
Charles Link said:
I can not follow what you are trying to do. If there is a lens involved with focal lengths and other parameters, please supply some more detail.

I'm trying to calculate If given 55 degrees and a run of .7 inches what's the number of (5177nm) pixels I can fit in that height?
 
  • #4
aneikei said:
I'm trying to calculate If given 55 degrees and a run of .7 inches what's the number of (5177nm) pixels I can fit in that height?
It would help to have a diagram. Most likely this is a fairly straightforward and simple geometry problem. A good diagram would be very helpful to see what is needed.
 
  • #5
Charles Link said:
It would help to have a diagram. Most likely this is a fairly straightforward and simple geometry problem. A good diagram would be very helpful to see what is needed.

Thank you for your help btw.

In the image, the angle is a static 55 degrees. At .7 inches there is less height than at 1 inch. At both, I want to know how many pixels that are 5177 nm in size can fit vertically at each position.
 

Attachments

  • angle.png
    angle.png
    5 KB · Views: 310
  • #6
## 2 \tan(\frac{55.11^{\circ}}{2})=\frac{h_1}{.7 }## and ## 2 \tan(\frac{55.11^{\circ}}{2})=\frac{h_2}{1} ##. ## \\ ## Number of pixels=## \frac{h}{d} ## where ## d= ## pixel size. ## \\ ## The height ## h ## is in inches, so to convert to nanometers : ## h_{nm}=h_{in} \cdot 2.54 \cdot 10^7 ##. ## \\ ## Number of pixels=## \frac{h_{nm}}{d_{nm}} ##. (You need to have the units be the same for both ## h ## and ## d ## ). ## \\ ## ## h_1 ## is the case of a distance of .7", and ## h_2 ## is the case of 1". ## \\ ## I don't really see the application of exactly what the purpose of this calculation is, but perhaps what I gave you is helpful. ## \\ ## In the future, I would recommend that this type of calculation belongs in the homework section (even if it isn't exactly homework). ## \\ ## I am going to ask the Moderators to move this post to the Homework section. In the Homework section, it is a requirement to fill out the homework template. In addition, the student is required to work to the solution, rather than the Homework Helper providing the solution. (See Physics Forums Rules).
 
  • #7
aneikei said:
In the image, the angle is a static 55 degrees. At .7 inches there is less height than at 1 inch. At both, I want to know how many pixels that are 5177 nm in size can fit vertically at each position.
What is confusing here is that you are mixing angles and distances when there doesn't seem to be any actual connection. 5177nm per pixel is 4906 pixels per inch. Period. It doesn't matter if it's .7 inches away or .7 miles away.

...unless there is something else you aren't telling us, like that this is a projected image...?
 
  • Like
Likes davenn and Charles Link
  • #8
Several people have mentioned the advantage of including a diagram. Everyone has some way of producing something adequate with the standard applications that you find on computers. Failing that, a photo of a felt tip on paper diagram would be better than nothing. PF can only work on the information you have provided. A diagram is essential in many situations.
 
  • Like
Likes Charles Link
  • #9
A pixel is a description of a surface. They have height and width, which don't have to be the same. If you know the dimensions you'll need two arc lengths: the base and the height setting the limits.
 
  • #10
I should say a rectangular surface, though other shapes are theoretically possible. Programmers set pixel size in most graphic programs.
 
  • #11
aneikei said:
Hello, I could some help. I've reached some sort of paradox. Ultimately I'm trying to calculate the number of pixels per inch, given a pixel size of 5177 nm and extended at a distance of .7inch (.0178 meters)

(A) (60 arcsecs * 0.0178 meters)/206268 = 5177nm pixel per arcmin

(B) 5177 * 60 = 310,620 nm per degree.

(C) tan(55)*.7 = 1 inch (thus 55 degrees = 1 inch)

(D) 310,620 * 55 = 17,084,100 nm per inch

(E) 17,084,100 nm /5177 nm = 3300ppi

However, 5177 nm = .000204 inch
and 1 inch / .000204 = 4901

Thus, 4901 x 5177nm = 25,377,450 nm per inch
25,377,450 nm /5177 nm = 4901 ppi
which is way different from 17,084,100 nm per inch
17,084,100 nm / 5177 nm = 3300 ppi

What did I do wrong? Which is correct? Thank you in advance

What you're doing wrong is that there aren't 17,084,100 nm per inch. There are 25,400,000. Somehow, both of your calculations are getting this wrong, though one is much closer than the other. You don't need to use angles or viewing distances at all.
 
  • #12
Are there other things called "pixels"? The original question said pixels.
 
  • #13
The etymology is derived from an elision of "picture elements". Pixel. They have at least two dimensions.
 
  • #14
Sanborn Chase said:
Are there other things called "pixels"? The original question said pixels.
reread post #1 then read post #7 for the correct explanation :smile:
 
  • #15
aneikei, are you trying to measure something with your camera?
 

What is the "Help - pixels per inch paradox"?

The "Help - pixels per inch paradox" is a common problem encountered in digital imaging, where the number of pixels per inch (PPI) in an image does not necessarily correspond to the image's quality or resolution.

Why is the "Help - pixels per inch paradox" important to understand?

Understanding the "Help - pixels per inch paradox" is important for anyone working with digital images, as it can impact the quality and appearance of the final image. It is especially important for those working with print media, as the PPI of an image can affect its print quality.

What causes the "Help - pixels per inch paradox"?

The "Help - pixels per inch paradox" is caused by the difference between the physical size of an image and its digital size. A digital image is made up of pixels, while a physical image is measured in inches. When these two measurements are not properly aligned, it can lead to confusion about the image's quality and resolution.

How can I avoid the "Help - pixels per inch paradox"?

To avoid the "Help - pixels per inch paradox," it is important to understand the relationship between PPI and image quality. It is also important to properly resize and resample images to ensure that they have the desired PPI for their intended use.

Are there any tools or resources available to help with the "Help - pixels per inch paradox"?

Yes, there are many tools and resources available to help with the "Help - pixels per inch paradox." These include image editing software with PPI settings, online calculators to determine optimal PPI for printing, and tutorials and guides on properly resizing and resampling images.

Similar threads

Replies
14
Views
989
Back
Top