PMC

Proof of π phase difference between the interference fringes at the primary and the secondary beam splitter exits. See Appendix for details.

Experimentally measured and rotationally averaged I⁵S OTFs O_m of for m= 0, ±1 and ±2 (A—C). (D) Demonstrates that m= 0 and m=±1 components partly overlap when they are placed where they belong in frequency space.

I⁵S illumination structure axial profiles in frequency space, obtained by deconvolving measured I⁵S detection OTF from the I⁵S effective OTFs. Black, red and blue curves correspond to order m= 0, ±1 and ±2 components, respectively.

The effective I⁵S OTFs were acquired through the primary and secondary beam splitter exit and rotationally averaged, and their additions and subtractions, for m= 0, ±1 and ±2, are shown in (A)–(C) and (D)–(E), respectively. The regions derived from the sidebands of the detection OTF are mostly missing in the additions, although those from the central band are missing in the subtractions, as theoretically predicted.

Results showing the effects of path length difference estimation and correction. (A) and (C) The axial profiles of I⁵S reconstruction of a single bead, imaged with intentional path length differences estimated to be 0.15 and −0.9 radians, respectively. (B) and (D) Results using synthesized OTFs based on the estimated path length differences corresponding to (A) and (C), respectively. There are significantly less ringing artefacts in (B) and (D) than in (A) and (C).

When the m= 1 component () is placed where it belongs in frequency space, it partly overlaps with the m= 0 component as indicated by the shaded areas. Shown here are only the regions because of the convolution of central band of the detection OTF (, green) and the central three and two frequencies of the m= 0 and 1 illumination structure, respectively ( and 4B).

Principles of I⁵S explained in frequency space. (A) The generalized pupil function (GPF) of an I⁵S/I⁵M microscope, i.e. the portions of the wavefront detectable through the two objective lenses. In a conventional widefield microscope, only one of the two shells is detectable. The support (i.e. region of nonzero value) of the intensity detection OTF, which is the autocorrelation of the GPF, is shown in (B). In comparison, the detection OTF of a conventional microscope is just the middle region. (C) The six dots represent the six collimated illumination beams being incident upon the sample. Their interference creates a 19-component illumination intensity pattern (D) organized into five vertical lines corresponding to m=−2 to 2. (E) The effective I⁵S OTF support is shown in k_y–k_z cross-section. As a reference, the conventional OTF support is drawn in dashed contour in (E).

The maps of phase values in I⁵S detection OTF (A), illumination structures (B) and the effective OTFs for m= 0 (C), ±1 (D) and ±2 (E). The reason why most illumination components are stretched axially compared to was explained in detail in earlier publications (; ). The regions coloured differently correspond to different phases equal to various linear combinations of a and b, where a and b are the phase differences caused by the path length difference in the interferometer loop for the excitation and emission wavelengths, respectively. In reality, the dashed lines in (C) and (D) coincide, i.e. they represent the same lateral frequency.

The schematic drawing of an I⁵S microscope. The illumination light passes first through a transmission grating, which diffracts it into three beams (green lines), and then through a beam splitter, which splits each beam and directs three beams to each of the two opposing objective lenses. The same beam splitter combines the two beams of emission light (red) from the sample onto the camera. Normally, only one camera (CCD 1) is used to record the emission light from one of the two beam splitter exit ports. Here we introduced a second imaging path to record on CCD 2 the emission light from the other exit port. The movable objective lens can be positioned in X, Y and Z with respect to the stationary objective lens. Mirrors M3 and M4 can be translated together to adjust the path length difference. The grating can be rotated and laterally translated to control the orientation and lateral phase of the illumination pattern. Mirrors M3 is made partially transmissive to let conventional illumination come in from there so that I⁵S detection OTF can be measured.