A light ray that strikes an object consisting of two mutually perpendicular reflecting surfaces is reflected back exactly parallel to the direction from which it came (Figure 1.9). This is true whenever the reflecting surfaces are perpendicular, and it is independent of the angle of incidence. (For proof, see [link] at the end of this section.) Such an object is called a corner reflector, since the light bounces from its inside corner. Corner reflectors are a subclass of retroreflectors, which all reflect rays back in the directions from which they came. Although the geometry of the proof is much more complex, corner reflectors can also be built with three mutually perpendicular reflecting surfaces and are useful in three-dimensional applications.

Image mtfformula

As a counterexample, if you are interested in building a stealth airplane, radar reflections should be minimized to evade detection. One of the design considerations would then be to avoid building 90°90° corners into the airframe.

When you see yourself in a mirror, it appears that the image is actually behind the mirror (Figure 1.8). We see the light coming from a direction determined by the law of reflection. The angles are such that the image is exactly the same distance behind the mirror as you stand in front of the mirror. If the mirror is on the wall of a room, the images in it are all behind the mirror, which can make the room seem bigger. Although these mirror images make objects appear to be where they cannot be (like behind a solid wall), the images are not figments of your imagination. Mirror images can be photographed and videotaped by instruments and look just as they do with our eyes (which are optical instruments themselves). The precise manner in which images are formed by mirrors and lenses is discussed in an upcoming chapter on Geometric Optics and Image Formation.

MTFlens

We expect to see reflections from smooth surfaces, but Figure 1.6 illustrates how a rough surface reflects light. Since the light strikes different parts of the surface at different angles, it is reflected in many different directions, or diffused. Diffused light is what allows us to see a sheet of paper from any angle, as shown in Figure 1.7(a). People, clothing, leaves, and walls all have rough surfaces and can be seen from all sides. A mirror, on the other hand, has a smooth surface (compared with the wavelength of light) and reflects light at specific angles, as illustrated in Figure 1.7(b). When the Moon reflects from a lake, as shown in Figure 1.7(c), a combination of these effects takes place.

Whenever we look into a mirror, or squint at sunlight glinting from a lake, we are seeing a reflection. When you look at a piece of white paper, you are seeing light scattered from it. Large telescopes use reflection to form an image of stars and other astronomical objects.

MITRE developed the MTF, SFR, and IQF freeware applications to support performance analysis of fingerprint capture devices and printers for FBI product certifications, for the FBI's Certified Products List* and the US government's Personal Identity Verification (PIV*) program. Corresponding to these certifications are available spec and test procedures [3.3MB]. These applications support development of devices enabling high accuracy examination, matching, and identification of fingerprints and interoperability across the forensics/law enforcement community.

Image mtfgraph

MITRE originally developed the IQM freeware application to support the US government's needs in image reconnaissance/surveillance and interpretation/exploitation. IQM correlates with NIIRS*, the traditional visual image interpretability rating scale used for such purposes. IQM is structured such that the user can tailor it for quality evaluation of other image types, e.g., pictorial, medical, image compression studies, etc.

MTF imagequality

Working on the same principle as these optical reflectors, corner reflectors are routinely used as radar reflectors (Figure 1.11) for radio-frequency applications. Under most circumstances, small boats made of fiberglass or wood do not strongly reflect radio waves emitted by radar systems. To make these boats visible to radar (to avoid collisions, for example), radar reflectors are attached to boats, usually in high places.

Modulation transfer functionimageprocessing

MITRE modified existing code to compute the Spatial Frequency Response (SFR) using an edge target, following procedures defined in ISO-12233*. The SFR equals the MTF of an imaging system under certain conditions.

MITRE is a registered trademark of The MITRE Corporation. Material on this site may be copied and distributed with permission only.

© Jul 23, 2024 OpenStax. Textbook content produced by OpenStax is licensed under a Creative Commons Attribution License . The OpenStax name, OpenStax logo, OpenStax book covers, OpenStax CNX name, and OpenStax CNX logo are not subject to the Creative Commons license and may not be reproduced without the prior and express written consent of Rice University.

MITRE developed its Image Quality Measure (IQM) application to directly measure the quality of an arbitrary image, i.e., it does not require imaging a specific target, constant scene, or reference image. IQM (overview.pdf) is computed from the image's spatial frequency power spectrum.

The law of reflection is illustrated in Figure 1.5, which also shows how the angle of incidence and angle of reflection are measured relative to the perpendicular to the surface at the point where the light ray strikes.

Image mtfcurve

Want to cite, share, or modify this book? This book uses the Creative Commons Attribution License and you must attribute OpenStax.

Many inexpensive reflector buttons on bicycles, cars, and warning signs have corner reflectors designed to return light in the direction from which it originated. Rather than simply reflecting light over a wide angle, retroreflection ensures high visibility if the observer and the light source are located together, such as a car’s driver and headlights. The Apollo astronauts placed a true corner reflector on the Moon (Figure 1.10). Laser signals from Earth can be bounced from that corner reflector to measure the gradually increasing distance to the Moon of a few centimeters per year.

This book may not be used in the training of large language models or otherwise be ingested into large language models or generative AI offerings without OpenStax's permission.

MITRE developed its MTF application to compute the Modulation Transfer Function of an imaging system using a sinewave target*, or compute the Contrast Transfer Function (CTF) using a bar target. Aliasing is detected and quantified and, for a sinewave, the input/output relation is established.