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Resource Page / 应用案例 / 成像 / Resolution and MTF Testing
Resolution and MTF Testing

Resolution and MTF Testing

Only a few decades ago, it was standard to find 640 horizontal pixels on camera sensors. Nowadays, it is common to see several thousand horizontal pixels. When sensors only offered several hundred pixels, it was customary for the imaging lens to outperform the sensor. Today, pixels on sensors are getting smaller and more numerous and sensors themselves are increasing in size. To keep up with sensors, lens manufacturers have increased their selection of lenses, while pushing the boundaries of lens design technology and manufacturing. To take advantage of pixels decreasing in size and increasing in number, lens performance must increase. Selecting the right lens requires understanding and proper characterization of a lens’s performance.

Measuring how well a lens performs requires the correct metrology. To characterize performance, a set of objectives based on lens specifications must be designated before selecting test methods. It is important to remember that no one test method can fully characterize every lens specification. Moreover, many tests that are useful in characterizing performance exclude real-world and often application-specific, external effects. Therefore, a test plan that uses multiple methods may be necessary

Resolution is often the most important specification for an imaging lens as it is a continuous function that tells the user how small a detail can be before it is indistinguishable from its surroundings at a specific contrast level. The performance of a lens can vary across different points within the image as well as with working distance, f/#, and other parameters. When measuring resolution and contrast, it is important to manage expectations and set reasonable system boundaries. Some resolution test methods can reveal additional information about other parameters, such as distortion and relative illumination. Common tests for lens resolution include reverse projection, modulation transfer function (MTF), slanted-edge MTF, and camera. Each of these methods provides a unique set of benefits and drawbacks.

Reverse Projection Testing

In reverse projection testing, a lens test projector is used to, essentially, image in reverse. The pattern from a high accuracy test target is placed at the image plane and is projected through an imaging lens to a specific working distance and observed in a dark room. Because the modulation of light through a lens is a reversible process, this method is a simple and effective test of resolution. It is also useful because resolution performance specifications are already given as image space values. A common test target used in reverse projection is the USAF 1951 target, which consists of several orthogonally oriented bars of increasing frequency that spiral into the center. The bars are dispersed across the entire field, allowing operators to focus the lens to optimize resolution at specific field regions. As such, this method can be used to test multiple field points at once.


Figure 1: An operator performing a reverse projection test. The circles labeled 11, 9, and 6 correspond to image circles of 2/3”, 1/1.8”, and 1/3” sensors, respectively.

Reverse projection is a low-cost and fast method to test lens resolution and astigmatism. Operator training is relatively easy, and the equipment is inexpensive compared to other methods. One important drawback of this test is the inability to measure contrast levels since this test method depends on operator eyesight. Human eyes can typically detect the lowest resolvable contrast, which is approximately 20%, but not specific contrast values.

Modulation Transfer Function (MTF) Testing

The most comprehensive representation of the resolution performance of an imaging lens is a modulation transfer function (MTF) curve. MTF curves are used to directly compare the resolution of one lens to another. Commercial test benches are available that allow for the characterization of lenses within a three-dimensional coordinate system (Figure 2).


Figure 2: Testing an imaging lens on a commercially available Trioptics branded MTF test station.

An operator conducts an MTF test by passing an impulse signal through a lens, typically in the form of light from a point-source against a dark background. Careful attention is paid to the position of the source and the location of the image. The impulse response is then used to determine a response at any spatial frequency up to the Nyquist (the highest resolvable sampled frequency). Because the testing environment is so tightly controlled, the measurements obtained are purely descriptive of the performance of the lens. External phenomena, such as stray light and falloff, are not factored into system-level performance specifications and the actual achievable resolution may be less than what the MTF curve suggests. Calculations from an MTF test bench are, by definition, contrast as a function of spatial frequency within a one, two, or three-dimensional coordinate system.

Slanted-Edge MTF Testing

Slanted-edge MTF testing obtains the same system level information as MTF testing but more quickly, with more adaptability, and on less expensive equipment. Regular MTF testing uses the Airy disk of a point-source magnified by an objective to fit the full sensor to remove any external MTF contributions but slanted-edge MTF testing uses a high contrast edge target positioned at an angle of several degrees. If only the MTF contribution of the lens is required, then all contributions from other components must be removed from the system level MTF (dividing them out because contributions are multiplicative). The first step in obtaining the slanted-edge MTF is to measure the sigmoidal-shaped edge-spread function. Once this function has been measured, its derivative is used to determine the line-spread function, which is then filtered and Fourier transformed into the MTF curve.


Figure 3: Testing an imaging lens on a commercially available Trioptics branded MTF test station.

This process only works if the contrast transition of the edge target occurs at a scale four times smaller than the Nyquist limit. If an edge target has a transition of 100μm and the resolution goal is 100lp/mm, (5μm Nyquist sample size), then the edge target would be enough as long as the magnification (m) is less than 0.0125X (see calculation).

$$ \left( \text{Transition Width} \right)_{\small{\text{Image Space}}} \left[ \text{μm} \right] < \text{Nyquist Width} \left[ \text{μm} \right] \div 4 $$
$$ \left( \text{Transition Width} \right)_{\small{\text{Object Space}}} \left[ \text{μm} \right] \times \textit{m} < \text{Nyquist Width} \left[ \text{μm} \right] \div 4 $$
$$ 100 \text{μm} \times \textit{m} < 5 \text{μm} \div 4 $$
$$ \textit{m} < \frac{5 \text{μm}}{100 \text{μm}} \div 4 $$
$$ \textit{m} < 0.0125 $$

Camera Tests

“Camera test” is an umbrella term for all tests that use a camera. The slanted-edge MTF test is one specific camera test but it is not the only common camera test for resolution. Camera test methods can be adapted, using different techniques or equipment, to any real-word application to obtain system-level, environmentally relevant resolution information. These often use test targets that allow for a specific set of performance metrics to be tested at the correct image-field positions and in the test environment.

Method Pros Cons
Rear Projection
   
Fast Qualitative
Inexpensive Poor diagnostic capabilities
Operator friendly  Poor ability to control spectral content (response is photopic) 
Tests multiple field points concurrently  Hard to maintain accurate coordinate systems 
 Quickly establish limiting resolution Difficult to use for higher magnifications 
 MTF    Off the shelt measurement instruments available  Calculated at one image point at a time
Higher-order aberrational content can be diagnosed  Insensitive to stray light and other environmental contrast degrading phenomena 
High accuracy and precision  Poor reproduction of most real-world illumination environments 
Most broadly-applicable "general use" test method  Expensive, easily misused equipment 
Slanted Edge MTF     Tests multiple field points concurrently  Target selection can be difficult for common magnification range (~0.05 - 0.01X)
Free and commercial software readily available    Sensitive to illumination uniformity
Can use a standard (ISO 12233) or tweak to suit specific needs  System-level contribution from non-lens components can lead to large error bars (especially at high frequencies) 
Can be used to measure system level MTF including lens, camera, illumination, and any image processing algorithms     Easily misused
  Coordinate system of cameras shifts from tangenital and sagittal performance to horizontal and vertical
 Camera Tests  Tests multiple field points concurrently  
The most application-specific approach  Little to no outside support 
Endlessly adaptable Difficult to correlate
Can be used to measure system level performance including lens, camera, illumination, and any image processing algorithms  
Table 1: The pros and cons of some of the most common lens performance test methods

As the number of smaller sized pixels continues to increase in sensors, the optical and mechanical requirements of lenses made to interface with them must also improve. System and machine vision end users often misunderstand the effects that govern vision system performance. Understanding what information each test method provides, as well as the pros and cons for each, will ensure success. 

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