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Basic Imaging Theory
Hurter and Driffield (H&D) Curves:
- The above curve is a typical H&D curve and is a plot of optical density versus the log of the exposure (sometimes it is called the characteristic film curve).
- Remember optical density is , where:
- I - is the amount of transmitted light through the film.
- Io - is the original amount of light before transmission through the film.
- A few characteristic effects should be considered:
- Fog - darkening of the film due to background radiation.
- Base - natural attenuation of a completely unexposed film.
- Speed - is a term that is related to the amount of radiation required to give an optical density of 1 above the base and fog. Fast films require little radiation; slow films require a lot. This is represented in the above figure which higher speed films corresponding to higher S values. (Note: diagnostic films are fast but films we use in therapy are slow).
- Gradient - is the slope of the curve in the linear portion (where you want to be for imaging and dosimetry tests) and is a measure of the contrast of a film (a high gradient means strong contrast, smaller changes in exposure result in larger changes in optical density).
- Latitude - refers to the range of exposures a film can accept and still produce contrast in the image (darkest to lightest). Underexposing or overexposing result in areas with very low gradients which would not be useful for establishing good contrast differentials.
Contrast to Noise Ratio (CNR):
- Contrast is defined as the difference in value between two objects on an image. This could take the form of optical density or Hounsfield units, etc., and is represented by A and B above.
- Noise is defined as the amount of fluctuation in an image due to statistical uncertainties and can be measured by looking at the standard deviation in pixel value over a uniform area (noise may come from photon counting or from electronics).
- If an image displays very little noise, subtle contrast differences can be seen, but if there is a lot of noise then more contrast is required to visualize a difference.
- Noise is directly influenceable by changing the amount of exposure an image is taken with as there is less statistical variation in a large number of photons.
- CNR is one of the most important imaging parameters as it is directly related to visually being able to see an object.
Modulation Transfer Function (MTF):
- The MTF is a mathematically derived quantity. In the simplest terms, it is a measure of perceived contrast versus object size. If you consider the above 3 curves as an object becomes smaller (increasing spatial frequency), it becomes harder and harder to visualize (decreasing contrast).
- Generally, the limit of perceivable contrast is considered an MTF of 0.1.
- Nyquist frequency - is the minimum frequency an object must be sampled to be visualized (it is generally considered to need to be sampled twice to be seen. In other words, the Nyquist frequency of an object is half its size. (Layman’s.... we need at least two pixels to be filled by an object to be able to see it).
- Aliasing - occurs when a high-frequency signal is sampled at a lower frequency (such as pixel binning, see below).