The circle of confusion

A large reason for image blur arises from simple geometry - the image point is not at the focal distance. Geometric blur is quantified by the size of the circle of confusion, which is the diameter of a point image. The function opticsCoC calculates the circle of confusion.

We semilogy the circle of confusion here for different F#s and Focal length lenses.

The depth of field is calculated from the CoC. One picks a criterion size for the CoC and finds the near and far points at the size. The distance between them is the depth of field. This DoF will vary with the optics and also with the distance of the point from the lens.

For a description of the Circle of Confusion [see this Wikipedia page](http://en.wikipedia.org/wiki/Circle_of_confusion#Determining_a_circle_of_confusion_diameter_from_the_object_field) It links to the original wonderful article describing the geometry.

See also: opticsCoC, opticsDoF, s_opticsDoF

Contents

ieInit

Calculate the circle of confusion diameter for different points

lineStyle = {'-','--'};
oDist = [0.5 3];  % meters

for oo = [1,2]

    % A 50 mm f# 2 lens
    fN = 2;
    fL = 0.050;
    optics = opticsCreate;
    optics = opticsSet(optics,'fnumber',fN);
    optics = opticsSet(optics,'focal length',fL);

    % Set the distance to the inplane focus
    [c, xDist] = opticsCoC(optics,oDist(oo),'unit','mm','n samples',50);

    hdl = ieNewGraphWin;

    % Plot the circle diameter as a function of distance
    semilogy(xDist,c,'b','LineStyle',lineStyle{oo}); grid on;
    xlabel('Object distance (m)');
    ylabel('Diameter of circle of confusion (mm)');

Shrink the aperture

    fN = 8;
    fL = 0.050;
    optics = opticsSet(optics,'fnumber',fN);
    optics = opticsSet(optics,'focal length',fL);

    % Set the distance to the inplane focus
    [c, xDist] = opticsCoC(optics,oDist(oo),'unit','mm','n samples',50);

    % Plot the circle diameter as a function of distance
    hold on;
    semilogy(xDist,c,'r','LineStyle',lineStyle(oo)); grid on;
    xlabel('Object distance (m)');
    ylabel('Diameter of circle of confusion (mm)')

Keep the same F# but change to focal length

    fN = 2;
    fL = 0.100;
    optics = opticsSet(optics,'fnumber',fN);
    optics = opticsSet(optics,'focal length',fL);

    % Set the distance to the inplane focus
    [c, xDist] = opticsCoC(optics,oDist(oo),'unit','mm','n samples',50);

    % Plot the circle diameter as a function of distance
    hold on;
    semilogy(xDist,c,'k','LineStyle',lineStyle(oo)); grid on;
    xlabel('Object distance (m)');
    ylabel('Diameter of circle of confusion (mm)')

    legend({'F# 2 FL 50 mm','F# 8 FL 50 mm','F# 2 FL 100 mm'});
    title(sprintf('Circle of Confusion - Focus distance %.1f m',oDist(oo)));
    drawnow;

end

Published with MATLAB® R2024a