Illustrated Physics
physics, drawn
Concept

Dynamic range — where it appears

The ratio between the strongest and the weakest signal an instrument can record at once, usually quoted in decibels. In ultrasound imaging it sets how deep an echo can still be heard, and so how many separate depths fit into one line of an image.

Named by 2 essays across 2 fields — each of them below, with the objects they name alongside it.

The rings belong to the edge, not to the size. The far-field intensity of 3 apertures of the same width, against angle in units of the diffraction limit, on a logarithmic intensity axis spanning ten decades. They differ only in how the transmission falls off toward the rim. With a hard edge the first sidelobe is 13.3 decibels down and the core is 0.89 wide. With a Hann taper the first sidelobe is 31.5 decibels down and the core is 1.44 wide. With a Blackman taper the first sidelobe is 58.1 decibels down and the core is 1.64 wide. The hard edge's rings are not a defect of the optics and are not reduced by making it larger — they are the transform of a discontinuity, and the only way to remove them is to remove the discontinuity. What it costs is the width of the core, which is the resolution.

The rings that belong to the edge

Every account of diffraction so far asks what the size of an aperture does. The rings around a star are not about its size: they are the transform of a discontinuity, they do not shrink relative to the core when the telescope grows, and the only way to remove them is to stop the transmission falling to zero abruptly. Softening the edge buys forty-five decibels of contrast and costs eighty per cent of the resolution.

optics · Diffraction A number of details that frequency cannot change. The number of separately resolvable depths along one line of an ultrasound image, the deepest echo divided by the axial resolution, against frequency, for dynamic ranges of 50, 60 and 80 dB in soft tissue; dashed, the same for a medium that absorbed like water, as the square of the frequency, with 60 dB. In tissue the count is D/(α₀Nc), the same at every frequency: 325 for 50 dB, 390 for 60 dB, 519 for 80 dB. It is a property of the tissue, through α₀, and of the electronics, through D, and changing the frequency only trades depth for sharpness one for one. In a medium with an f² law the count would fall as 1/f, from 88,548 at 1 MHz to 1,771 at 50 MHz. It is the near-linear absorption of tissue that makes the trade exact.

The depth an ultrasound image pays for its sharpness

An ultrasound scanner sees finer detail at higher frequencies, because shorter waves make shorter pulses, and sees less deep, because tissue absorbs higher frequencies more strongly. Both effects scale as one over the frequency, so they cancel in the one number that matters: how many separate depths fit along a line of the image. For soft tissue, which absorbs nearly in proportion to frequency, that number is about four hundred whatever the frequency — set by the tissue and by the scanner's electronics and by nothing else. A scan of the abdomen at three megahertz and a scan of the skin at fifty are the same picture at different magnifications.

waves · Attenuation

Named alongside it

The objects these essays reach for when they reach for this one.

Acoustic attenuationApertureApodisationAxial resolutionContrastCoronagraphDiffractionFourier transformHarmonic imagingPoint-spread functionPower law absorptionPulse echo imaging

All concepts