During the design of an optical system, the Modulation Transfer Function (MTF) of a lens is an important factor in the selection process. However, the sensor used also contributes to the MTF of the system. Adimec has developed a new MTF measurement system that can measure the MTF of the sensor separate from the lens. This blog will explain this MTF measurement method and how to analyse the MTF graph.
MTF and resolution
The ability of an optical system to distinguish details can be defined in either spatial or spectral terms. Commonly, the resolution of a sensor is described in megapixels. This is a physical spatial sample property of the sensor and describes how much detail of an object is captured. The MTF of a sensor is the ability to distinguish spaced line pairs. This is a spectral measure. Resolution contributes to the MTF, but other properties of silicon influence the MTF of the sensor as well.
The diagram below illustrates the concept of MTF. Here, a camera is focused on the red lines. The video level over the pixels is seen in the camera output section. When contrasting lines are placed closer to each other, the frequency is higher, and the details become smaller.
To distinguish high frequency lines, the resolution needs to be increased. The MTF describes the contrast between the line and no line as a function of frequency. See the website of Edmund Optics for a more detailed explanation of the MTF.
The MTF can be measured in absolute terms or relative terms. The relative MTF measurement is the most common method. It uses a lens to focus the camera on lines with different frequencies. At every frequency the contrast between the line and no line is measured as illustrated before. The result of this data is the MTF. The drawback of this method is that the camera is focused using a lens. This will result in an MTF where the interaction between the lens and image sensor is captured as well.
Adimec has therefore developed an absolute MTF measurement setup, which can measure the MTF of the image sensor only. The absolute measurement method uses an indirect way of measuring the MTF. This means that instead of measuring the contrast and the frequency of the lines, we now use a single line to focus on. Using different mathematical functions, this signal is transformed into the MTF.
MTF of an image sensor
Measuring the MTF of an image sensor in absolute terms has multiple advantages. For one, it is possible to determine the specific performance of a sensor and compare it with other sensors. One might expect that the MTF only depends on the resolution of a sensor. That is not the case. MTF strongly depends on the sensor architecture (Front Side Illumination or Back Side Illumination), the pixel fill, and the addition of micro lenses. Furthermore, the MTF is not the same for all wavelengths. Detailed MTF information for the sensor at a specified wavelength can be used to predict the performance of the optical system in your application. All of these parameters are captured by the absolute MTF.
The MTF is not only an important benchmark for the performance of an image sensor — it is also used to determine the specifications needed for your optical system. You can use a high-resolution sensor, but the lens quality should also match the sensor to reach the best performance and cost-effectiveness. The resolution of an image sensor is expressed in megapixels. However, the resolution of a lens is commonly measured in line pair per millimetre, i.e. the frequency of lines over a millimetre. Thus, measuring the MTF of the image sensor makes it possible to compare the spectral resolution of the image sensor and optical system more precisely by using the same unit of measurement.
How to read an MTF curve
As said earlier, the absolute MTF measurement supplies the information required to determine the performance of the sensor. In this example, we analyse the MTF of the Sony IMX25X series.
However, as has been noted before, the MTF does not only depend on the resolution. If it did, the red line would exactly follow the theoretical line. Due to design choices made by the manufacturer, the measured MTF deviates from the theoretical.
If your application requires better performance at a higher frequency, a lens can be selected that has a higher MTF then the image sensor. However, this will result in a more costly lens. It is important to note that when selecting a lens, the manufacturing tolerances of the lens need to be taken into consideration. In addition, the aberration due to wavelength difference should also be considered for both the image sensor as well as the lens.
The last component in the graph is the Aliasing frequency of the system, also called the Nyquist frequency. Frequencies before and after this point are no longer distinguishable from each other, because the lines after the Nyquist frequency are too close for the sensor pixels to resolve the signal.
When designing your optical system, the sensor should be chosen such that the working range of the application is within the Nyquist frequency. Machine vision applications generally do not use the available data after the Nyquist frequency. When selecting the lens, the MTF of the lens must be applicable within the working range. For example, when inspecting displays, often a lens is chosen with an MTF curve that ends at the aliasing frequency.
The MTF is a measure influenced by more than resolution. It also includes sensor design and contrast differences. Adimec has developed a measurement method for measuring the MTF of an image sensor without the lens. Therefore, it can support its customers with information that was not available before. This information is of great interest when designing an optical system or when comparing multiple image sensors.