Optics Distortion as applied to Machine Vision

INTRODUCTION
This third paper by Adept Electronic Solutions in the series on Optics as applied to Machine Vision discusses the aberrations and distortions that are introduced by lenses and other optic components when used in machine vision systems. It discusses distortions not only in the spatial domain but also those in the spectral (frequency) domain. Any questions and comments are welcome. For more detailed information or an explanation of anything in this paper please contact us at AES.

The first two papers on Optics can be found at these links:

Depth of Field

MTF

LENS ABERRATIONS

VIGNETTING
Lenses do not transmit intensity evenly over the whole image. They vary in intensity from the centre to the outside edges of the image. The centre of the image is brighter than the edges. As this will typically affect Machine Vision tasks it is important to quantify or at least consider the amount of vignetting when selecting a lens. Vignetting is usually described by plotting the Relative Illumination against the Angle of View. The Angle of View is defined as the angle of light rays measured against the optical axis - the axis from the centre of the image to the centre of the object.

There are three different mechanisms that may be responsible for Vignetting. Natural and optical vignetting are inherent to each lens design. The third, mechanical vignetting is due to mechanical constraints within the lens. Natural vignetting is due to the natural decrease in illumination from the centre to the edge of the image. Optical vignetting is caused by the nature of the lens being less efficient at collecting light at the edges of the image. Natural and optical vignetting lead to a gradual transition from a brighter image centre to darker corners. At large apertures both phenomena are present and the combined effect is often designated by the term 'illumination fall-off'. Mechanical vignetting can also give rise to gradual fall-off, although the usual connotation is one where it causes an abrupt transition with entirely black image corners. Reducing the size of the iris can significantly reduce the effect of vignetting. In quantifying vignetting fully it is therefore necessary to represent several vignetting plots at different apertures as indicated in the graphs above.

DISTORTION
Distortion is defined as the change in geometrical representation of an object in the image. A rectangular object might be reproduced as a pincushion or a barrel in the image. A pincushion image is represented as a positive distortion. A barrel shaped image is represented as a negative distortion. Distortion, positive or negative, may change from the centre to the edges of the image. Distortion is specified as a %. Measured as (Predicted Size-Actual Size)/Predicted Size x 100. Distortion is affected by the Magnification (Focal Length) of a lens. Shorter focal length lenses typically introduce more distortion.

SPECTRAL TRANSMISSION
Optical materials (glass, plastic etc) transmit wavelengths at varying efficiencies. Some wavelengths are absorbed or reflected in varying amounts. Optical lenses are manufactured from Optical Glass. A precision lens is typically made up of a number of different lens elements and each of these may be made from different glass types. Each glass type may have different spectral qualities and so the combination of elements will produce a distinct spectral transmission curve. It is important to evaluate the transmission data for any potential lens.

Here are some examples for consideration:
a) Consider the spectral response of the camera sensor. Using a lens that tends to block the wavelengths of light, at which the camera sensor is most sensitive, will decrease overall system sensitivity and reduce performance.
b) When measuring extremely small features it can be useful to use ultraviolet wavelengths. Wavelengths below 400nm allow finer definition in the image. Glass tends to block UV and suitable lenses require appropriate coatings to transmit UV.
c) Silicon sensors found in many industrial cameras are sensitive to Infrared (IR) wavelengths. The human eye is insensitive to IR but if using a CCD camera in low light situations the use of IR wavelengths is beneficial to sensitivity. When selecting a lens for this situation care must be taken to select one with extended transmission into the near Infrared.

CHROMATIC ABERRATION
The different wavelengths or colour of light are refracted in varying amounts and this effect produces defects in an image called Chromatic Aberrations. A great deal of the complexity of modern lenses is due to efforts (mostly successful) of lens designers to reduce Chromatic Aberration. There are two types of Chromatic Aberration, Longitudinal and Lateral.

1) Longitudinal (Axial) Chromatic Aberration is described as the effect caused by the lens' inability to focus different wavelengths of light in the same image plane.

It can be seen from the illustration that a lens can be re-focussed for chromatic aberration to produce optimum performance for various wavelengths. This can be done successfully with monochromatic light. With white light however, the different wavelengths have different focal points and so produce a less sharp image.

2) Lateral Chromatic Aberration results in a lateral shift in the image. This results in colour stripes around hard edges, and a general softening or a general decrease in MTF or resolution in all areas.

The moral to the colour story is that if a vision system is not required to measure or differentiate colour it can be advantageous to use a monochromatic or narrow band light source eg. Red Leds, as this will reduce chromatic aberrations resulting in sharper images.

SPECTRAL WEIGHTING OF IMAGE QUALITY
The Modulation Transfer Function of a lens will change significantly dependent on the wavelengths of light in use. A number of factors such as the chromatic aberrations and the effectiveness of the anti-reflection coatings for various wavelengths contribute to this effect. Typically a lens will work better with monochromatic light than with a full spectrum. Therefore when evaluating a lens it is important to do so with precisely the light to be used in the vision application. This is usually referred to as Spectral Weighting.

CONCLUSION
The discussion above aims at uncovering most of the major sources of lens aberrations. It discusses (albeit briefly) all of the considerations with respect to aberrations when selecting a lens. Often however it is difficult to find all of the quantitative data for a lens that allows a system designer to make a qualified theoretical decision on lens selection. In general you will find that quality lens manufacturers publish detailed data relating to the specification of their lenses, whereas lower quality lens manufacturers normally do not. CCTV lens manufacturers very rarely do. Hence the advice from you experienced vision supplier can be paramount in making the correct decision.

NEXT PAPER
The next paper wraps up these previous three papers and steps through the process of selecting a lens in a logical and sequential manner.

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