Reconstructed Data Checks

Reconstructed Intensity Histogram (RIH)

Displays an overlay of linearly- and logarithmically-scaled intensity histograms (black and gray, respectively) showing relative contribution of “negative” values to the reconstructed result for each channel. Negative values are those below the average (mode) intensity value for background regions, and are due to reconstructed noise and ringing artefacts at the edge of high-intensity features. The Max-to-Min intensity Ratio (MMR; positive versus negative intensities at the histogram extrema) is reported: i.e. only a small percentage of the highest and lowest intensities (this increases the robustness of the statistic to differences in the proprtion of background versus features in the image). A ratio less than 3 generally indicates poor reconstruction; a ratio above 6 indicates good reconstruction.

N.B. This check requires a non-thresholded reconstructed dataset: any option that discards low intensities, such as “discard negatives” in GE’s SoftWoRx software, should be disabled.

RIH histogram and image for good reconstruction RIH histogram and image for poor reconstruction

Figure 3a. Reconstructed images and intensity histograms for a good (left) and poor (right) reconstruction. The histogram peak corresponds to the centre of the background intensity distribution, i.e. reconstructed noise. Ideally this peak should be narrow. Intensity information for real features should extend in the positive direction only, which it clearly does to a greater extent in the histogram on the left.

Spherical Aberration Mismatch (SAM)

This check is not enabled by default, as it requires an appropriate sample, e.g. a bead lawn, to work reliably.

The SAM check plots the minimum and the mean value in each slice, and summarizes the standard deviation of the minimum value normalized by the stack mode intensity, the Z Minimum Variation (ZMV). Large variations in the minimum value relative to the average indicate mismatch between the spherical aberration present when the sample and point spread function data were acquired.

SAM plot and image without mismatch SAM plot and image with mismatch

Figure 3b. Reconstructed images and slice mean/min plots for a reconstruction without (left) and with (right) spherical aberration mismatch. A characteristic dip in the minimum value indicating mismatch is shown with a red arrow in the bottom right plot. This corresponds to the dark (negative) fringe around the edge of the nucleus, also marked with a red arrow in the image data top right.

Fourier plots (FTL, FTR, FTO)

Note that this check evaluates the image volume’s average characteristics. It is therefore recommended to select an image region with a high proportion of features as well as some background. A very high proportion of background can make it difficult to discern the contribution from the features of interest.

Displays 2D Fourier transform “target” plots with overlaid resolution lines (in Microns) and optionally blurred and color-coded with a 16-color look-up table to make the relative proportion of different frequencies more obvious. The plots displayed are: Fourier Transform Lateral (FTL) for XY sections; Fourier Transform Radial (FTR) which is a radial (circularly-averaged) profile though the XY Fourier Trasform; and optionally, Fourier Transform Orthogonal (FTO) for the central resliced XZ section (N.B. ensure the central Y point contains some features of interest). These plots help judge the average resolution in the sample volume, limited by noise. A gradual decay of frequencies from the center (lowest frequency) to the edge (highest frequency and resolution) indicates real high resolution information; whereas a flat spectrum indicates predominantly noise at the higher frequencies. The lateral (FTL) and radial (FTR) plots give an indication on XY resolution, while the axial (FTO) plot reports on Z resolution as well.

FTL plot for a high resolution image FTL plot for a low resolution image FTO plot for the high resolution image FTR plot for a high resolution image FTR plot for a low resolution image

Figure 3c. The top row shows 2D Fourier transform amplitudes (log- scaled). Top left: a high resolution dataset; middle: a noisy, low resolution dataset showing a “hard edge” (red arrow) and obvious “flower pattern”; right: 2D Fourier transform of an orthogonally resliced (i.e. axial) cross-section through the image, which reports on Z resolution. Bottom: radial profile plots derived from the lateral Fourier transform images in the top row. In the FTR plot for the left-hand high resolution image, frequency amplitudes decay smoothly until 1/8 to 1/10 microns, i.e. a resolution of ~120 nm. In the poorer middle dataset, frequency amplitudes decay rapidly, disappearing into the noise by ~200 nm. The second, rapid drop at 125-100 nm corresponds to the frequency support limit of the OTF.

Reconstruction artifacts may also be apparent as spots in the Fourier spectrum, which are observed as regular, repeating patterns in the image.

FTL plot showing spots (artifacts)

Figure 3d. An image containing reconstruction artifacts shown top left, with a blow-up of top right of the image shown bottom right. Spots are evident in the 2D Fourier transform “FTL” plot, highlighted with a red arrow. In the reconstructed image these reconstuction artifacts can be seen as repeating hexagonal patterns.

When run as a stand-alone plugin, there are a number of options to configure. The default display option is to apply a cut-off at the modal intensity value before Fourier transformation, which is equivalent to “Discard Negatives” in the OMX reconstruction software or “Baseline Cut / Shifted” in the ELYRA reconstruction software. Default is to display the FFT amplitude, gamma-scaled (gamma=0.2). Other options are:

  • Cut-off: manual, which is equivalent to thresholding the image at the intensity value(s) chosen (i.e. if thresholding at an intensity value other than the modal intensity is necessary).

  • Window function, which reduces spurious high frequencies in the FFT of images with features that reach to the edges of the image.

  • 32-bit Amp, gamma 0.2, display min-max, which is the same as the default option, but with a final display scaling step based on image content.

  • 8-bit log(Amp^2), display mode-max, which is similar to ImageJ’s default FFT “power spectrum” display, and 1) emphasies high frequencies; 2) produces a result that takes up less memory (i.e. may be useful for large datasets).

  • Blur & false-color LUT (described above, off by default)

  • Show axial FFT (described above, off by default)

Modulation Contrast Map (MCM)

This plugin produces an RGB image displaying a combination of intensity information and modulation contrast calculated from the raw data: i.e. the proportion of red, green and blue is adjusted to reflect modulation contrast (<3 purple, to 6 red, to 12 orange, to 18 yellow, to 24 white), and the overall intensity of each pixel is scaled according to intensity in the reconstructed image. Features that are red-orange, yellow or white (i.e. MCNR >6) can be considered reliable. Additionally, pixels that are saturated in the raw data are colored green in this map. Note that ImageJ shows the R,G,B pixel values in its status bar when you hover over a pixel with the pointer. It is intended as a quantitative tool for assessing whether individual features in the reconstructed data are supported by the raw data.

MCM map highlighting high and low resolution microtubules.

Figure 3e. Modulation Contrast Map for a MicroTubule (MT) sample. Note the Look-Up Table at the bottom right of the image shows the corresponding modulation contrast value for each color. A MT filament with low modulation contrast (0-6, purple-red) is highlighted with a red arrow: this implies lower resolution / less reliable high resolution features than microtubles with a modulation contrast >6 (orange/yellow/white).