MTF and NPS Flashcards
In general, what does the modulation transfer function (MTF) describe? What would the MTF of a perfect system be?
The reduction in ‘gain’ of a system when a signal of a given spatial frequency and 100% modulation (i.e. black and white) applied to the input of a system. At the output, the modulation may be less than 100% depending on the spatial frequency. A perfect system would have 100% modulation at all spatial frequencies.
What happens to the MTF at high spatial frequencies?
The output modulation becomes comparable to the noise present in the system. Sharp edges are less distinct making features harder to distinguish.
How can MTF be measured? What assumptions are made?
- By imaging a high-contrast edge.
- After passing through the imaging system, the edge will no longer be quite so sharp and the resulting edge-spread function can be used to measure MTF via differentiation to line spread function and then Fourier transform.
- Assumptions include that the system is linear and the impulse response does not vary with position (shift invariance).
What is an issue with MTF measurement for a digital system? How is this avoided? What limits this work around?
- The detection element prior to the pixel matrix is able to pass more frequency information to the pixel grid than the grid is capable of sampling. This violates shift invariance and leads to problems with aliasing. The maximum frequency that can be sampled is related to the pixel size and is termed the Nyquist frequency. Any information above this cut-off gets folded back into data and results artificially increasing the MTF at high spatial frequencies.
- This is avoided by imaging the edge at an angle to the pixel matrix so it is sampled at a slightly different place on each pixel row or column. This increases the effective number of pixels across the edge.
- Noise is accounted for by taking the average for each pixel row. As there are fewer rows available for averaging with the change in angle, the MTF will become more noisy, thus limiting this work around. There is a trade-off required.
What is the effect of oversampling on MTF curves?
Spatial frequency is increased. This is important as the pre-sampled MTF may extend beyond the Nyquist limit imposed by the pixel matrix.
What aspects of a flat panel detector limit the pre-sampled MTF response?
- Input aperture.
- Crystal layer aperture (CsI/a-Se).
- Coupling between CsI and light sensor in such detector types.
What effect does smoothing have on the MTF?
Will reduce noise but also correspond to poorer resolution (i.e. MTF cut-off at lower spatial frequency).
How does edge enhancement affect an MTF?
Edge enhancement amplifies a portion of the MTF curve at higher spatial frequencies (no increase in spatial frequency, however).
What does the noise power spectrum (NPS) display?
How much variance (power - noise^2) is present in the image per spatial frequency channel.
How is the normalised NPS obtained?
- Flat field image cut into number of smaller squares.
- Fast Fourier transform (FFT) processing is applied.
- The NNPS from each square is then averaged to form the final result.
- Normally data is extracted and presented in 1D.
How does normalised NPS vary as detector dose increases?
- NNPS proportional to 1/SNR^2.
- Given definition of SNR with respect to N, NNPS is, therefore, proportional to 1/dose.
- => NNPS decreased. However, noise increases. The NNPS shows how the noise varies relative to the signal.
What effect will smoothing and edge enhancement have on NNPS?
- Smoothing: Noise reduced at higher spatial frequencies.
- Edge enhancement: Noise increased at higher spatial frequencies.
