Circle of confusion of a micro four third camera

Circle of confusion

Circle of confusion

In photography, the circle of confusion (AKA CoC) is the limit of blur points viewed as one point by the human eyes. So if you register points smaller than the circle of confusion, you won’t be able to see them on a screen or on a printed image unless you use some magnifier or have done a cropping in the editing process.

In the above image the 3 blue spots won’t be distinguishable as they are of a lower size than the circle of confusion illustrated by the red circle.

The Circle of Confusion depend on the size of the viewed image (either on screen or printed) and the distance used to view the image. For the human eyes, the best closest comfortable viewing distance is 25cm and the image resolution of a normal human eye is 0.2mm at this distance. When enlarged without cropping, a sharp image need to be seen from a greater distance to be seen always as sharp.

As the Circle of Confusion is used in the formula which allow to determine the depth of field of an objective, I need it to find the theoretical depth increment between 2 shots in a focus staking process of water mite. In the formula found on the Nikon website, the important CoC is the CoC at the captor level and so I wanted to know it for my Panasonic Gh1. Even if the Wikipedia give a CoC of 0.015mm for the four third system, I wanted to do my own calculations.

Calculation of the CoC of my Panasonic GH1

File image width pixel 1000 My usual setting for web IWF
Size on screen (mm) 200 Measure on a 17″ screen IWS
coc (mm) 0.2 Found in Wikipedia – Human limit HCoC
width in CoC 1000 Number of lines of the viewed image IWS/HCoC
CoC (pixel on screen) 1 CoC on the screen. Normal result IWF/(IWS/HCoC)
Captor width (pixel) 4000 Depends on the camera sensor CWp
Captor width (mm) 17.3 For the Panasonic GH1 CW
CoC captor (pixel) 4.00 Number of pixels on captor for oe unit of CoC CWp/IWF*HCoC
Coc captor (µm) 17.3 Circle of confusion on the captor CW*1000/(IWS/HCoC)

To determine my captor CoC I measured on my computer screen an image of 1000pixel of width. 1000 pixels is my common setting when I’m editing an image for web publication. This image of 1000 pixel was measured at roughly 20cm of width on my screen.

This image of 1000 pixels viewed at a distance of 25cm and as the CoC of the human eye is 0.2mm at this distance allow to see only 200mm / 0.2mm = 1000 points on the screen. This show that an image of 1000 pixels of size is just OK for been seen enlarged to 20cm and viewed from 25cm. With this setting it seems that there is neither lost pixel neither too much pixels for publishing my pictures of water mites. In other word, one pixel of the image file match perfectly the capacity of the human eye resolution when viewed in this conditions.

As the captor can record images of 4000 pixels of width (specification of my camera Panasonic GH1 – micro four third), that implies that the limit of useful resolution at the captor level is 4000/1000 = 4 pixels. Thus in µm, as the 4000 pixels of the captor are lodged in a width of 17.3mm (or 17300 µm) we have a CoC of 17300 / 1000 = 17.3 µm on the GH1 captor. This not far away from the CoC of 0.015mm considered as the circle of confusion for the micro four third camera (Wikipedia).

It’s also interesting to see that with tis CoC of 17.3µm, there are 4 pixels of width to register one point. This means a square of 16 pixels and as each pixel usually record only one color, we need at least a square of 4 pixel to get a good idea of the color of a point. With these 17.3µm, we are not using the whole capacity of the camera sensor.

References.

  • Wikipedia : complete article on the circle of confusion
  • A nikon page with the formula to determine the depth of field of a microscope objective

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