Optics Resolution applied to Machine Vision

• Introduction
• Summary of Depth of Field Paper
• Image Quality
• Lens Quality
• Resolution
• Contrast
• Modulation Transfer Function
1. MTF Graph
2. MTF and the CCD Sensor
3. Location of MTF
4. Tangential and Sagittal Lines
5. Resolution and D.O.F Compromise
• Next Paper

INTRODUCTION

This is the second in a series of discussion papers by Adept Electronic Solutions Pty Ltd that talks about aspects of machine vision. We welcome comments, questions and any criticisms. If you want further explanation of anything in this paper please contact us.

The paper commences with a brief summary of the first paper presented on Depth Of Field. It goes on to discuss what defines image quality and what factors affect a len’s quality. The concepts of resolution and contrast and their relationship are then discussed. The Modulation Transfer Function is defined and an example of how to match it to a CCD sensor is given. Finally the paper discusses the MTF with respect to where it is measured in the image.

SUMMARY OF DEPTH OF FIELD PAPER

The key points to come out of the first paper on Depth Of Field are:

1. Depth Of Field is defined as the range of distance from the camera, from near to far, which appears to be in focus.
2. In order to quantify Depth Of Field the Circle of Confusion (Diffraction Spot size) must first be defined and quantified. The first is meaningless without the second.
3. Circle Of Confusion defines what is in focus versus what is out of focus.
4. The smaller the pixel of the camera sensor, the smaller the Circle of Confusion of the lens needs to be in order to optimise the resolution of the system.
5. One of the laws of optics is that the Depth Of Field extends from one third in front of the point focused on, to two thirds behind it.
6. Depth Of Field is inversely related to the magnification of the image.

IMAGE QUALITY

The physical variables that can affect the quality of an image are:

• Lens quality
• Lighting
• Sensor resolution
• Sensor pixel bit depth and noise
• Sensor mosaic filter type vs 3CCD vs monochrome
• Sensor alignment - camera manufacturing tolerances
• Camera and/or subject motion

LENS QUALITY

An ideal lens would be one that replicates an object exactly. An ideal lens would transfer all of the details of the object to the image without any variations. In the "real world" this ideal lens does not exist and we must deal with real lenses that produce slight variations between the object and the image.

The quality of a lens can not be measured as a single number or described in a single statement. There are a number of factors that determine the quality of a lens:

• Sharpness / Resolution
• Contrast
• Colour correction
• Relative illumination
• Spectral transmission
• Distortion.

RESOLUTION

The Resolution of a lens (optical resolution) is quite easily defined as the ability of the lens to transmit a certain degree of detail in a target object. Coarse structures ( such as coarsely spaced lines ) are usually transferred more easily than fine structures. Resolution is usually measured in lines (or line pairs) per millimetre where a line pair is defined as a black and white line of equal width.

Resolution is closely related to Circle of Confusion as defined in the first paper on Depth Of Field. The larger the Circle of Confusion of a lens then the lower is its ability to resolve line pairs (resolution). It is useful to note that 75 line pairs per millimetre (lp/mm) is getting up towards the limit of the very best lenses. It is also useful to note that prime (fixed focal length) lenses are sharper than zoom lenses. Zoom lenses have more elements than primes which makes them more difficult to design. It increases the risk of optical aberration and can reduce resolution and contrast.

In the real world there is not just "black and white" and so the concept of contrast must be introduced in order to quantify resolution as they are intimately related.

CONTRAST

Contrast (acutance or modulation) is just as important if not more important than resolution in producing a good quality image for machine vision. A high quality lens with good resolution will typically have good contrast quality as well but cannot be assumed.

Contrast is the measure of the difference in grey value or colour in an image and is very closely related to resolution when discussing the quality of an image. Contrast is not about resolving detail but is about the transition between edges. In other words when an edge changes from one brightness level to another. In order to measure features of objects in an image it is typically edges that define a feature and the quality ( resolution and contrast) of the edges that govern measurement accuracy.

The effect of diminishing contrast with spatial resolutions is described.

It is useful to graph the way that contrast varies with spatial frequency. This is called the Modulation Transfer Function. The MTF is perhaps the one most useful piece of data when specifying a lens.

MODULATION TRANSFER FUNCTION

MTF GRAPH

The MTF can be characterised as the len’s ability to transfer contrast from the viewed object to the sensor. It maps contrast against resolution i.e. as line pairs get more closely spaced the noise between them blurs the edges and makes the black lines look dark grey and the white lines look light grey as can be seen in the image above.

The MTF graph plots the contrast on the Y-axis as a percentage of the original object contrast, versus spatial resolution ( line pairs / mm ) on the x-axis. It is clear that the contrast decreases as the spatial resolution increases until it reaches a point where the contrast is zero. This is often called the resolution limit or the resolving power of the lens. Beware of using this number only. A lens may have a high resolving power however may have poor modulation (contrast) at low spatial resolution rendering it poor for many vision applications. Ideally the lens should have a relatively high contrast over the range of spatial resolutions required for the application. Typically for machine this is the pixel size or pixel pitch of the CCD sensor.

For example: Ideally the lens will provide high contrast at a spatial resolution that equals the spatial resolution of the CCD sensor so that if considering line pairs the black line fits one pixel and the white line fits the pixel next to it. So for a sensor with a 7 micron pixel size a line pair needs to cover 14 micron which translates to a resolution of 1/14 micron = 71 lp/mm.

MTF AND THE CCD SENSOR

It is useful to note here that the smaller the pixel size (or pitch) of the CCD, the higher the resolving power required by the lens. With the current trend to smaller CCD sensors in the CCTV industry there is more and more pressure being put on the performance of the lens. For this reason it is important to consider machine vision cameras versus CCTV cameras for machine vision work.

LOCATION OF MTF

A single MTF graph represents the PTF performance of lens at a single point in the image. Typically a single MTF graph from a supplier represents the MTF at the centre of the image. In order to evaluate the MTF of a lens over all of the image, a number of MTF graphs need to be provided. These are typically plotted for different positions in the image from the centre along the diagonal to the image corner.

TANGENTIAL AND SAGITTAL LINES

The MTF will also differ with the orientation of the line pairs. Typically this is characterised with different MTF graphs for both Tangential and Sagittal line directions. Sagittal lines are parallel to the diagonal direction in an image and tangential are perpendicular to the diagonals.

RESOLUTION AND D.O.F COMPROMISE

As was explained in the first paper the f-stop of a lens will affect the depth of field. An increasing f-stop number will give an increasing depth of field but conversely it will give a decreasing resolution. The larger the f-stop number then the lower the resolution. There is a balance between resolution and depth of field that must be struck when selecting light levels and f-stop.

The reduction in resolution due to f-stop can best be explained as follows:
As the f-stop number is increased the aperture (iris) of the lens closes (gets smaller). As the aperture gets smaller the effects due to diffraction and dispersion get larger and so affect resolution. A more detailed description of this effect will require an explanation of optical wavefront behaviour and is beyond the scope of this paper.

NEXT PAPER

In the next paper on Optics we will discuss some other aspects of a lens that affect image quality such as vignetting, colour aberration, distortion etc.