2000 Class Project

Christine S. Law

Effects of Polarization on Modulation Transfer Function

PowerPoint Presentation:   Effects of Polarization on MTF

Modulation Transfer Function (MTF) is the scientific means of evaluating the fundamental spatial resolution performance of an imaging system, or components of that system.  A polarizer lens filter is an essential tool for outdoor photography.  The purpose of this project is to understand the effect of a polarizer upon the MTF of a charge coupled device (CCD) camera.  The polarizer deepens intensity of blue skies; reduces or eliminates glare.  I have a Ricoh CCD camera; however, it doesn't come with threads for mounting external filters.  As a photographer, I like to use polarizer whenever it is possible.

A light wave is an electromagnetic wave which travels through the vacuum of outer space. Light waves are produced by vibrating electric charges.   A light wave which is vibrating in more than one plane simultaneously is referred to as unpolarized light. Light emitted by the sun, by a lamp, or by a candle flame is unpolarized light.

Unpolarized light can undergo polarization by reflection off non-metallic surfaces. The extent to which polarization occurs is dependent upon the angle at which the light approaches the surface and upon the material which the surface is made of.  Non-metallic surfaces such as asphalt roadways, snow fields and water reflect light such that there is a large concentration of vibrations in a plane parallel to the reflecting surface. A person viewing objects by means of light reflected off of non-metallic surfaces will often perceive a glare if the extent of polarization is large. Fisherman are familiar with this glare since it prevents them from seeing fish which lie below the water. Light reflected off a lake is partially polarized in a direction parallel to the water's surface. Fisherman know that the use of glare-reducing sunglasses with the proper polarization axis allows for the blocking of this partially polarized light. By blocking the plane-polarized light, the glare is reduced and the fisherman can more easily see fish located under the water.

Spatial detail can be measured by the spatial frequency content of a given feature. A good example of this is the frequency of the line features in any vertical line bar target group as shown in Figure 1. Each of the vertical line groups in a target represents a different spatial frequency. For example, the group at the upper left hand corner has a frequency of 1.0 line pairs per millimeter (1.0 lpmm). A line pair (dark-line/white-space combination) is more universally referred to as "one cycle". For this example then, one cycle (line pair) spans 1/1 = 1.0 mm. The higher the frequency, the greater the detail, the greater the number of cycles per unit distance, and the more closely spaced the lines become.

Though square wave signals are easy to manufacture into targets and can be used to measure MTF when properly treated, alone they are not considered to be basic image building blocks. As such it is technically incorrect to use them as reference signals in determining MTFs. Properly, sine-waves are used. For simplicity, however,  square wave is used for all  measurements.

Square wave frequencies, in units of lpmm, are used as the metric for specifying detail in an MTF plot. These frequencies are always plotted as the independent variable on the x-axis. To complete the MTF metric, a measure is required of how well each square wave frequency is preserved after being imaged, that is, transferred through an imaging device. This measure, called modulation transfer, is plotted along the y-axis for each available frequency and completes the specification of MTF.

The modulation for any signal is defined with two variables of that signal, the maximum light intensity value, I_max, and minimum light intensity value, I_min. Modulation or relative contrast is formulated as the quotient of their differences to their sums, as follows:

Modulation or Relative Contrast =	(Imax - Imin)
	(Imax + Imin)

The goal in determining MTF is to measure how well the input modulation is preserved after being imaged or in some way acted upon. This modulation transfer is quantified by comparing the modulations of the output square waves after being imaged, to the target's input square wave modulations before being imaged. This comparison is a simple ratio of output modulation to input modulation. It is formulated as:
 
 

Very often, we keep the input modulation as unity and it is indeed used for all measurements.

A simple way to interpret the modulation transfer is by thinking of it as a measure of how well the camera preserves the average contrast of each input square wave frequency. A modulation transfer of 1 indicates that the average contrast for a given square wave frequency is perfectly maintained, while zero modulation transfer shows that it was completely lost, or not "seen" in the imaging process. Values between 0 and 1 indicate varying degrees of contrast preservation. Though there are exceptions, generally, the higher the modulation transfer, the better the preservation of detail by the imaging system.
 

Methods

I added a Kodak lens adapter to my Ricoh camera.  The Kodak lens adapter allows the attachment of any 37mm filter.  Since 37mm is not a standard size for filters, I also use a 37mm to 49 mm step up before adding a 49 mm polarizer.

MTF Measurement Technologies

There are many methods for measuring MTF -- for example, discrete or continuous frequency generation, imaging scanning, and wavefront analysis.

Frequency Generation Methods

The most direct and common test of MTF is to capture the image of an object that consists of a pattern having a single spatial frequency.  Then we can measure the contrast of the image directly.  Discrete frequency measurements can be made using bar charts, resolution targets, and eye charts.  A series of such tests can be used to create a graph of MTF over a range of spatial frequencies.  This method is used for this project and the measurement details are discussed below.
 

A test pattern as shown in Figure 1 is used as test input for the MTF.  It contains square waves having spatial frequencies from 1 lpmm to 14 lpmm.  Other test images include the same square wave pattern with same spatial frequencies varying in the vertical direction, and the same square wave pattern but using black and cyan instead of black and white.
Figure 1

Each line bar target group in Figure 1 has only one single frequency; however, the lower three groups may seem to have more than one frequency.  This is because the maximum spatial resolution of the monitor is lower than the spatial frequency of the line group represented.  This is also known as aliasing.  MTF limitation by the system spatial resolution will be explained in the following section.

All test patterns are captured with the Ricoh camera twice: once with the polarizer and once without.  For each output image, the relative contrast of the imaged  square wave is measured and the results are plotted in Figure 2  , Figure 3 ,  Figure 4 , and Figure 5.

The measured MTF results show that little effect is caused by the polarizer; the average MTF reduction by the polarizer is about 5%.  Using black and cyan instead of black and white in the input test target also reduces the measured MTF by some amount.  In all cases, the Ricoh CCD sensor shows a better MTF response to vertical spatial stimulus than horizontal stimulus.

What is limiting the MTF?

The MTF for an ideal optical system is unity for spatial frequencies from 0 to infinity at every point and direction.  MTF can vary with almost every conceivable parameter, including f-stop, object distance, distance of the point from the center, direction of modulation, and spectral distribution of the light.

For a CCD camera, the MTF also suffers from the limitation of pixel size, dynamic range of the pixels, and pixel crosstalk.  In other words, pixel size limits the maximum resolution of a CCD camera.  A CCD sensor can transmit its maximum line pair number only if a dark bar falls specifically on a pixel and a bright bar on the neighboring pixel.  Thus, the maximum line pair number, which a sensor with a pixel dimension "p" can transmit, is

                                        LPMM_max = 1/(2p)

For example, a CCD sensor of the size 24 X 36 mm with 2000 X 3000 pixels will have a pixel size of 12 um.  The highest number of line pairs that the sensor can transmit is therefore 40 lpmm.

The pixel size of the Ricoh camera is estimated to be 20 um.  The maximum line pair number it can capture without aliasing is therefore about 25 lpmm.

How does the polarizer affect MTF?

The polarizer reduces the amount of light being detected by the CCD sensor.  Depending on the angle of incidence of the light, all pixels may not be fully utilized.  Since the magnitude of the input light is smaller than that without the polarizer, the percentage of error is relatively higher.  Also, optical distortion of the polarizer itself will degrade the MTF measurement.

What about the black-cyan MTF?

Using cyan instead of white in the input target reduces the amount of input light intensity, hence the MTF measurement error will in turn be greater.  The actual reduction in input light intensity depends on the CCD sensor mosaic and geometry.

Polarization filtering seems to have little effect on the MTF of a CCD camera.  The average MTF reduction by the polarization filter is about 5%.  The MTF of a CCD camera is not only limited by its optical components (lenses), but also by the pixel dimension.  Currently, the size of the smallest reproducible CCD structures are about 0.25 um.  It would be interesting to repeat the experiment with a higher resolution CCD camera and determine the effects of polarization filter (or other types of optical filters) on the image quality.

References

Wandell, Brain A., Foundations of Vision. Sunderland, Mass., 1995.
 http://www.research.ibm.com/journal/rd/423/melcher.html
 CCD imaging paper
 http://www.optikos.com/classes/pdfs/how_to_measure_mtf.pdf
 http://photo.net/photo/optics/lensTutorial.html

 plotting files    contains matlab files used in generating plots in this articles.
 profile              contains matlab files used to see the cross section profiles of an image.
 create_mtf       contains matlab files used to generate mtf data.
 bw_patch.m     matlab file used to create square wave patterns
 average.m        matlab file used to determine the relative contrast of a square wave.  It ignores data fall outside 1 std away from the mean.
 

PowerPoint Presentation:  Effects of Polarization on MTF