The Optical Transfer Function (OTF) is an important specification of lens performance. The OTF describes both the amplitude and the phase of a signal. In most cases the former, most times indicated as is Modulation Transfer Function (MTF), suffices. Modulation, as it is a measure of the modulation depth (contrast) of an optical signal. The MTF is for that reason sometimes also called Contrast Transfer Function (CTF).
Talking about the MTF of optics, say a lens, it is the reduction in modulation depth, starting with a modulation depth of hundred percent, due to that optics. The MTF of an optic is usually depicted versus the spatial frequency. Generally speaking the MTF drops with increasing frequency, which frequency is indicated as cycles or line pairs per mm (square-wave signal).
“The modulation transfer function is a measure of the transfer of modulation (or contrast) from the subject to the image. In other words, it measures how faithfully the lens reproduces (or transfers) detail from the object to the image produced by the lens.“
The MTF can be measured in various ways, either directly or indirectly. In case of direct measurement, a sine- or square-wave signal is used. In case of indirect measurement, a step, line or point source, of in principle infinite steepness is used. From the spatial light distribution after passing the optics, which will no longer be infinite, one can obtain the MTF via Fourier transform.
Besides the spatial frequency, the MTF strongly depends on the lens aperture, the light spectrum, the optical conjugation (e.g. magnification), field position, temperature and last but not least the level of optical correction of the lens itself (its quality so to say).
So while MTF is widely accepted as an important factor with lens selection, it is often not considered with the sensor/camera selection. MTF provides an indication of the sharpness of the image or image quality and is determined by both the lens AND the sensor.
The MTF of the image sensor should not be overlooked when comparing image sensor technologies, especially when working in the Near Infra Red (NIR) spectrum where there are big differences. The MTF of the lens and sensor varies with wavelengths which can be characterized using MTF-curves. The problem is that sensor manufacturers do not always (read “hardly ever”) specify MTF or when they do, it is only at a wavelength where QE is at maximum value (is close to the best case scenario). The MTF of all sensors at 550 nm is similar, but at longer wavelengths, the MTF of a sensor can be lower compared to other sensors. For some sensors, for instance, the MTF is reduced by a factor of 2 or 3 at 850 nm.
The amount of MTF reduction strongly depends on sensor technology:
- CCD / CMOS
- Front Side Illumination (FSI) / Back Side Illumination (BSI)
- With Microlenses / Without Microlenses
- And many manufacturing process parameters
Lower MTF limits the resolution of the system as a result of which small details of objects are no longer discernable, and this is wavelength dependent. In some cases this can be overcome to some extent by decreasing the noise level, which additional to MTF also causes a reduction in contrast, by increasing the light level.
In general, CCD technology has better MTF in NIR because of higher electric fields in the depletion layer, and deep-P diffusions for isolation of the columns in the Interline Transfer (IT) structure (compared with standard CMOS pixel design). Click here for more information on CCD vs. CMOS in defense applications.
Experienced camera manufacturers will have measured the MTF of the implemented sensor for the full wavelength range and can make the appropriate recommendations for your application.
Special contribution by René Aartsen, Adimec Electro-Optical System Designer.