Simple image normalization dramatically improves Transport-of-Intensity (TIE)-derived phase images

Quantitative phase mapping can be obtained by solving the Transport-of-Intensity equation (TIE) for two brightfield images I1 and I2 taken at two defocus distances. Phase restoration by TIE is based on the gradient of axial intensity, which is approximated by the difference I1-I2. The results of computation, however, are very sensitive to slight fluctuations of intensity between I1 and I2, resulting in spatially variable background and difficulty in analyzing the data. We found that the quality of phase images can be drastically improved by manually equalizing the intensities of the input images before processing. The tolerance of the computed phase to the choice of focal planes can be further improved by using the average of multiple time-lapse images to represent each of I1 and I2. With this simple modification, TIE microscopy can be easily applied to various biological problems. Introduction Quantitative phase imaging comprises a group of techniques for measuring the phase delay of a light wave crossing a sample (Popescu, 2011). One potentially important application of quantitative phase is determination of the refractive index of the cell, which is directly related to intracellular water and dry mass content. These parameters can vary independently from the total cell volume, and their knowledge is necessary to separate, for example, cell dehydration from cell fragmentation during apoptosis (Model and Schonbrun, 2013). The method of phase restoration based on the transport-of-intensity equation (TIE) is particularly attractive due to its simple technical realization. TIE quantitatively expresses the well-known fact that visibility of refractive index-mismatched objects changes with defocusing. Specifically, it relates the gradient of intensity I in the axial direction to the phase delay : ∂Ixy ∂z = − λ 2π ∇ ∙ (I∇φxy) In practice, one collects at least two brightfield images I1 and I2 at different distances to the sample, and the difference between them is used to approximate the gradient ∂I ∂z (Ishizuka and Allman, 2005). If sample thickness or volume is known from separate measurements (e.g., from confocal scanning, AFM or transmission-through-dye imaging (TTD)), the refractive index can be found. The main problem with TIE is sometimes poor quality and uneven background intensity of phase images resulting from noise (Paganin et al, 2004). This can significantly complicate quantitative analysis. More advanced computational methods based on multiple images have been developed to alleviate this problem (Waller et al, 2010). Here we report that phase images generated by the basic TIE algorithm can be improved substantially by simply equalizing the background levels in the two brightfield images used for gradient estimation. For example, if the average background pixel intensity is 2500 for I1 and 2503 for I2, then adding 3 units to I1 will markedly flatten the background and make analysis more reliable. Reducing noise by averaging multiple images of the same field to represent I1 and I2 brings about additional improvement. Methods Images were collected with a 12-bit cooled SensiCam QE CCD camera (Cooke, Romulus, MI) mounted on an inverted Olympus IX81 microscope. Illumination was provided by a quartzhalogen lamp through a NA0.5 condenser and a 485/10 bandpass filter (Omega Optical, Brattleboro, VT). The hardware was controlled by Slidebook (Intelligent Imaging Innovations, Denver, CO, USA). HeLa cells were grown on #1.5 coverslips and mounted in DMEM on a slide over a small amount of silicone grease. Single or multiple images were collected at several vertical positions and analyzed with ImageJ (http://rsbweb.nih.gov/ij/); TIE processing was performed on MatLab R2012b (MathWorks, Natick, MA) using the code published by Gorthi and Schonbrun (2012). To measure cells on phase images (as in Table 1), a contour with area A was drawn around the cell, and the average cell was determined within the contour; next, the average background level bkg was determined on a 3-m band adjacent to the contour, and the total phase was calculated as A(cell bkg). This procedure ensures consistent integral values (though not the means). Results and Discussion Processing of raw images (Fig. 1A, 1B) produced uneven background across the phase images (Fig. 1C). These artifacts are mainly caused by slight intensity variations between successive planes. Because in the absence of any objects the intensity should not change with defocusing, the background must ideally remain constant. (Importantly, the intensity of the entire image does not have to be conserved if cells are present near the edge). This is typically the case when the same field is collected multiple times in rapid succession and averaged (however, we have noticed that the first few images in a sequence were brighter than the rest; those images can be discarded before averaging). The improvement resulting from averaging is obvious from comparing Fig. 1C and Fig. 1D. Single images can also be corrected by measuring the background and manually adding or subtracting the difference before computing the phase (Fig. 1E). Uniform background facilitates image analysis. Table 1 lists the measurements of the integrated phase of one cell for various selections of input images. Measurements on raw images obtained with a 10x/0.4 objective resulted in widely divergent values for the phase. By contrast, the numbers were quite consistent when image averaging was used, especially when the planes within ~4 m of the visually best focus were used. Manual background adjustment on single images was less efficient but still produced a marked improvement over uncorrected images. Results with averaged images obtained with a 20x/0.7 objective were similar but less tolerant to excessively short object distances. To additionally demonstrate the origin of uneven background, we started with the averaged images corresponding to planes 1 and 3. All the pixels in image B were increased or decreased by 3 or 6 gray scale units, and the intensity profiles along the diagonal were determined (Fig. 2). While the profile was ideally flat when the average intensities of the two images were within one unit, the background bulged or caved for mismatched intensities. When larger cell clusters are present, they may produce local shading. However, by carefully adjusting the intensity levels, a reasonably even background can be achieved (Fig. 3). The same figure shows a good correlation between the phase and the cell height; the latter was obtained by TTD imaging (Model, 2012). Of course, such correlation is only expected for uniform and healthy cells; when cells, for example, are undergoing apoptosis the mismatch between phase and thickness can be used to quantify changes in cell water and dry mass (Model and Schonbrun, 2013). Figure 1. The original brightfield images (A, B) of HeLa cells collected with a 10x/0.4 objective and the results of phase restoration (C-E). A and B correspond to planes 1 and 3 in Table 1 separated vertically by 5 m. The arrow points at the cell whose measurements are presented in Table 1. Panel C shows the phase map based on uncorrected brightfield images, D is based on the average of 20 images and E is based on single images but with intensities manually equalized. The scale bar is 20 m. Figure 2. The effect of intensity mismatch on phase restoration. The central image c is the same as in Fig. 1D. Phase images a, b, d and e have been obtained by changing the intensity of the second image (B in Fig. 1) by -6, -3, +3 and +6, respectively (the average intensity of the image was 3000). The intensity profiles along the diagonal from bottom left to top right are shown. Figure 3. Brightfield images of HeLa cells BF1 and BF2 were collected with a 20x/0.7 objective. The vertical separation between BF1 and BF2 was 5 m. The phase image was computed after reducing the intensity of BF2 by 0.25 gray scale units. The TTD image of the same cells showing their height was collected in the presence of 7 mg/ml Acid Blue 9 added to DMEM and using illumination through a 630/10 bandpass filter, as described earlier (Model, 2012). The length of the scale bar is 25 m. Acknowedgements The authors thank Dr. Ethan Schonbrun for providing the MatLab code and Dr. Laura Waller for discussions of TIE. The research was supported by the University Research Council grant to MM.