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Jan/Feb, 2024


Image Processing: Optimized Balancing of Resolution and Depth of Field


By Dr. Claudia Link, Head of Optics Development, Vision & Control GmbH T


he two most important variables in image processing are a pair of apparent opposites. Maximizing just one of them alone will not lead to success. Instead, skillful juggling of the laws of optics is what is required. Image processing often


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demands both: maximum res- olution and perfect depth of field. Unfortunately though, these key optical parameters work against each other. Only by skillfully balancing aperture, wavelength, and image scale is it possible to achieve the best possible imaging for every task.


High-Res and Short Wavelength


Even on a lens with no


1. Min 0 1. Min Rho’ Figure 1: As defined in the


Rayleigh criterion, the limit of res- olution is reached when max and min illumination intensity on adjacent image points coincide.


8:30:23 AM


aberration errors, the resolu- tion capacity is limited by dif- fraction. An object point is always displayed by the opti- cal system as a diffraction disk with a bright center sur- rounded by light and dark interference rings. The radius in microns of


this disk, which is known as an Airy disk, is determined by multiplying the wavelength of the radiated light with the f-


stop and a factor of 1.22. If two adjacent image points are offset by the radius of this Airy disk, the bright center of the first point will coin-


WESTBOND’s New 7KF 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.1 Image scale


Figure 3: Resolution in the object plane for different image scales at a wavelength of 550 nm.


the limiting resolution based on the Rayleigh criterion. The pixel res- olution of the sensor should be at least twice this. For a common pixel size of 3.45 µm, this therefore means that the structure needs to be


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cide exactly with the first minimum of the other. This means that the Rayleigh criterion is met and the limit is


reached at which the two points can be comfortably distinguished with the eye. As well as keeping the f-stop as small as possible, the wave- length of the light- ing system plays a decisive role. With green light (550 nm), two adjacent points at a distance of 5.4 µm can still be distinguished. If blue light is used (450 nm), this dis- tance can be re - duced to 4.4 µm. In many cases,


a’


the required resolu- tion and the field of vision are already predefined. For example, if a structure measuring 5 µm still needs to be displayed with high contrast, then its image must be larger than


Figure 2: if an object point is shifted by the value a’ out of the image plane, this produces a circle of confusion u’. The magnitude of the resulting circles of con- fusion u’1 and u’2 is proportional to the aperture diameters D1 and D2.


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Figure 4: Depth of field for different image scales and aperture values, with a circle of confusion diameter of 20 µm.


imaged at a size of at least 7 µm — better still 10 µm. This makes an image scale of 2 necessary.


Increased Depth The image with maximum sharpness is only produced in the


image plane. However, real objects are rarely completely flat. This Continued on next page


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k k


k k k


k


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Resolution limit, object side


D2 D1


u’2 u’1


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