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FVCML0208 10

RESOLUTION MEASUREMENT AND ITS UNITS

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MEGAPIXEL
We start with a very common mistake.  “This camera has 10 megapixel resolution” is something you read here and there and often in ads, but from the technical perceptive this is wrong. A camera with 10 megapixel has ten million pixel that will sample the image that the lens has projected on the sensor. But this does not mean, that each pixel really holds a useful information about the image content. So the amount of pixel is somewhat related to the resolution, but does not define it. It is not uncommon, that a good 10 megapixel camera has the same resolution compared to a 12 or 14 megapixel camera.
LP/mm
In the analog times, the resolution of film and/or lens was expressed in line pairs per millimeter (LP/mm). This unit expresses the amount of line pairs you can find within one millimeter in the sensor/film plane. One line pair is a black line and a white line next to each other in the same orientation and with the same width. If you have 100 LP/mm resolution of a lens, this means that one find 100 black and 100 white lines within 1 mm projected on the film (or sensor).
The problem in the digital world? Digital values have no physical extent, only their representations on a screen or in a print. So you can not use this unit to express the resolution in a digital image. You can use LP/mm to express the resolution of a lens. But in this case you need to know the exact dimension of the sensor that is used in the device which is sometimes hard to find out and most of the times impossible if you can not open the device. Or have you ever seen the sensor in your mobile phone?
LP/pix (cy/px) LP/PH
As we have shown that LP/mm is not a suitable unit for the resolution a digital camera can capture, a different unit is needed. One very common unit is line pairs per pixel or cycles per pixel. In this case we do not have a physical extent in the unit, we just describe how many line pairs can be resolved by one pixel. As a line pair is always a black and a white line, the maximum resolution one can achieve is 1/2 LP/pix. So if one camera can resolve 0.4 LP/pix it reaches 80% of its theoretical maximum resolution. This way one can easily compare two camera and see how well they make use of the amount of pixel they have. If you only express the resolution in LP/pix, you do not take into account that the sampling itself will reduce the resolution. So if you have camera A with 0.5 LP/pix and camera B with 0.4 LP/pix you would say that A is better than B. But if camera A has only 320 pixel in height and camera A has 2000 pixel, camera B will definitely show more details in the same scene. So to make the test results comparable with the efficiency (LP/pix) and the amount of pixel combined, express the resolution as line pairs per picture height. In this example, this would result in a comparison of 160 LP/PH to 1600 LP/PH.
PPI MEGAHERTZ
Scanner prefer another unit: PPI, pixel per inch. In case of a scanner it express the amount of pixel that sample one inch (25.4 mm) of the scanned original. So if you test the resolution of that device, you need to know the size of object you scan. PPI is similar to “Megapixel”. It gives the amount of pixel used for one inch, but that does not mean that these pixel hold useful information. In our experience most scanner do not reach the promised sampling rate defined in PPI. So for a scanner, it is very intersting to check for the LP/pix, as this gives you the performance of the scanner. A lot of scanner get close to 0.5 LP/pix for 200 PPI, but get much less for 300 PPI or even 400 PPI. Just to mention as it is very often mixed up and used wrong: DPI is not the same as PPI. An ink-jet printer can have a very high DPI (dots per inch), but as it uses several dots to bring one pixel onto the paper, this is not equivalent to PPI. Megahertz as a unit for spatial resolution? In analog video, Megahertz is a known unit for the resolution as you have a well defined time per line. Other than in digital video, you do not have well defined pixel when you transfer the signal. So you can express the width of an image better in µseconds and if you replace the mm in LP/mm with µseconds, you end up with Megahertz.


*There are several methods to measure the MTF and/or the SFR and all of these methods have their own advantages and disadvantages. See conference paper »

 

UNITS AND CONVERSIONS FOR RESOLUTION

Resolition is measured using edges, Siemens stars or other regular structures with aíncreasing frequencies. Units like LW/PH, LP/PH, or Cycles per pixel are independent of the sensor size and the pixel pitch. They just take the resulting image and its frequency content into account not caring about the size of each pixel. Dimensions like LP/mm, L/mm, or Cycles/mm require the knowledge about the sensor size / pixel pitch.

The following table and explanation will be part of the upcoming revision of ISO 12233 and was created by Don Williams.

LW/PH = Line width per picture height
LP/mm = Line pairs per millimetre
L/mm = Lines per millimetre
Cycles/mm = Cycles per millimetre
Cycles/pixel = Cycles per pixel
LP/PH = Linepairs per picture height

To convert from left column units to top row units use operation at their row/column intersection.

Spatial Frequency Unit Conversion Chart

LW/PH LP/mm L/mm Cycles/mm Cycles/pixel LP/PH
LW/PH x 1 / [2 x picture height] / picture height / [2 x picture height] / [2 x # vert. pixel] / 2.0
LP/mm x [2 x picture height] x 1 x 2.0 x 1 x pixel pitch x [picture height]
L/mm x picture height x 0.5 x 1 x 0.5 x [pixel pitch / 2] x [picture height / 2]
Cycles/mm x [2 x picture height] x 1 x 2.0 x 1 x pixel pitch x [picture height]
Cycles/pixel x [2 x # vert. pixel] / pixel pitch x [2 / pixel pitch] / pixel pitch x 1 x [# vert. pixel]
LP/PH x 2.0 / picture height 2 / picture height / picture height / # vert. pixel x1

 

NOTE 1
The pixel pitch in the 45 degree diagonal direction is not the same as in the vertical and horizontal directions. Therefore, the diagonal pixel pitch is used when applying this table to measurements in the diagonal directions

NOTE 2
There are three planes for determination of the resolution in e.g. LP/mm. It can be in the object space, on the sensor plane or in the image with a given output magnification. In most cases the resolution on the sensor plane is the important one. To get the right value for this situation the image file should be scaled to the Sensor dimension in which case the pixel pitch on the sensor is equal to the pitch of pixels in the image file.

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