Table 2 Error metrics for real space and Fourier space data, for the case where the lower (“reference”) half of the crystal is assumed to be imperfect.

From: Deterministic Bragg Coherent Diffraction Imaging

Types of imperfection

Maximum phase (rad) due to parabolic displacement field

Minimum amplitude due to spherical inclusions

Normalised RMS error (d_ph) for reconstructed phase

Normalised absolute error (r_ph) for reconstructed phase

Normalised RMS error (d_amp) for reconstructed amplitude

Normalised absolute error (r_amp) for reconstructed amplitude

Error metric (χ 2) in Fourier space

original model for a displacement field throughout the crystal (ideal bottom half of the crystal)

0.25

0

0.1

0.2

0.6

0.1

1 × 10−5

displacement field exists in the entire crystal (bottom half of the crystal is deformed)

0.25

0

0.7

0.6

2

0.2

3 × 10−3

displacement field throughout the crystal and a slice 1pix(X) × 16pix(Z) × 64pix(Y) is removed from the bottom part of the crystal

0.25

0

0.7

0.6

4

0.2

3 × 10−3

displacement field throughout the crystal and a slice 32pix(X) × 1pix(Z) × 64pix(Y) is removed from the bottom part of the crystal

0.25

0

0.8

0.6

5

0.3

3 × 10−3

  1. Maximum intensity is 109 photons per voxel. The brightest voxel, corresponding to the origin of Fourier space, was excluded from the noise adding procedure as the appropriate intensity is multiplied by zero (see equation (11)) during the reconstruction process. Successive rows consider an ideal lower half of the crystal (as assumed by our reconstruction algorithm), followed by three different forms of departure from this assumed ideality. Weak displacement field and strong spherical inclusions are assumed throughout. For each case, five different error metrics (specified in equations (16), (17) and (18) of the main text) are given.
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