Modulation Transfer Function Explained (MTF)
MTF (Modulation Transfer Function) has been a topic of discussion lately. Here’s a breakdown of what it means in a basic sense.
MTF can be thought of as a measure of contrast at given intervals of spatial resolution. To understand this we need to understand what spatial resolution is. In Night Vision this is known as line pairs per millimeter (lp/mm). A line pair consists of a dark line and a bright line. ⬛️⬜️ much like these two squares. A line pair of 1 lp/mm means these two squares fit into 1mm of space. As only two are in this space the contrast of black and white is easily detectable. We will call this a 100% contrast.
As we move further along the spatial resolution scale we need to put more pairs into the same mm of space (increasing frequency). In order to do so these squares (line pairs) need to become thinner. As they become thinner (higher frequency) the ability to perceive the contrast between them diminishes. A bunch of these line pairs in the same millimeter of space will begin to be perceived as gray as the contrast between them becomes less detectable.
Plotting each measurement of contrast percentage detected in relation to spatial resolution on a graph with the y axis being contrast and x axis being spatial resolution (lp/mm) yields a curve. This is known as the MTF curve. As we increase spatial resolution (lp/mm) we decrease detectable contrast. This relationship or response is known as the Modulation Transfer Function.
Image Source: Photonis
The human eye can observe up to a 2-5% contrast difference in line pairs. When the curve approaches the limits of detectable contrast the eye is no longer able to discern a difference from that point onwards. This is the limiting resolution for a human observer (expressed in lp/mm). Most of you know this as the center resolution on your data sheet. Often 57, 64, 72, 81, etc lp/mm. As it is determined by a human observer, the limiting resolution is subjective to a small degree. Imaging systems can also evaluate resolution, though a human observer can usually resolve better. The two letters in the ID column of L3H data sheets are the initials of the human observer that tested your tube.
You may have noticed L3H data sheets have high light resolution listed (usually 36-45 lp/mm). MTF functions in the same way here. For Photonis Echo tubes the high light resolution isn’t listed, but they all have a minimum 50-57 lp/mm (depending on your country). From the two resolutions (high light and center) we can extrapolate a rough judgment of “how good” the MTF curve is. Elbit tubes do not have high light resolution listed, but they can be equated to L3H for the most part.
Wrapping up - A higher MTF expression is good. It means more contrast is preserved at a given frequency of spatial resolution. MTF does not determine the ability to detect contrast. Rather, it is the measurement/s of how well contrast is detected. Unfortunately, MTF is not reflected on data sheets at this time but is measured during production and testing.