Unit Conversion

Unit Conversion#

In order to simplify usage, reconstructions are done using arbitrary length units (ALU). In this system, 1 ALU can correspond to any convenient measure of distance chosen by the user.

Default Parameter Example: By default, when the CT model is constructed, the spacing between detector channels is set to 1 ALU. However, the detector channel spacing can be changed by setting the delta_det_channel parameter.

So if we reconstruct CT data from a scanner with detector channel spacing of 0.25 mm, with this default behavior, then delta_det_channel=1.0 and we interpret this as 1 ALU = 0.25 mm. In this case, the MBIRJAX reconstruction will be a 3D JAX array recon in units of \(\mbox{ALU}^{-1}\).

However, this can be converted to conventional units of \(\mbox{mm}^{-1}\) with the following scaling:

\[\mbox{(recon in units of mm$^{-1}$)} = \frac{ \mbox{recon in units of ALU$^{-1}$} }{ 0.25 \mbox{mm} / \mbox{ALU}} = \mbox{4.0*recon}\]

NSI Reconstruction Example: The NSI preprocessing functions in Preprocessing set all the parameters to the units used by NSI which are in mm. In this case, 1 ALU = 1 mm and the reconstructions will have units of \(\mbox{mm}^{-1}\).

In order to convert to units of \(\mbox{cm}^{-1}\), we use the following scaling:

\[\mbox{(recon in units of cm$^{-1}$)} = \frac{ \mbox{recon in units of ALU$^{-1}$} }{ \mbox{1 cm} / \mbox{10 mm}} = \mbox{10 *recon}\]

Zeiss Reconstruction Example: The Zeiss Versa preprocessing functions in Preprocessing allow the user to select units of either “um”, “mm”, “cm”, or “m”, with the default being “mm”. In this default case, 1 ALU = 1 mm and reconstructions will have units of \(\mbox{mm}^{-1}\).

Emission CT Example: Once again, we assume that the channel spacing in the detector is 0.25 mm, and we again assume the default reconstruction parameters of delta_det_channel=1.0. So we have that 1 ALU = 0.25 mm.

Using this convention, the 3D array, recon, will be in units of photons/AU. However, the image can be converted to units of photons/mm using the following equation:

\[\mbox{(recon in units of photons/mm)} = \frac{ \mbox{recon in units of photons/ALU} }{ 0.25 \mbox{mm} / \mbox{ALU}} = 4.0* \mbox{recon}\]