“Precise color” MFM. (a) Layout of MFM system with two arms, separated by a dichroic beam-splitting mirror. Each arm contains an MFG tailored to the wavelength spectrum of the fluorophore imaged to maximize signal strength and obtain equal focal shift in both colors simultaneously. The Chromatic Correction Module (CCM) consists of a multi-panel blazed grating that is specially designed to compensate for the dispersion of the MFG, and a multi-faceted prism to direct the images to their proper positions on the camera. (b) Layout of MFM data as acquired on the camera. (c) MFM data layout from b cropped out and arranged as a 3D volume. (d) Point spread functions (PSFs) of 100 ± 7.2 nm fluorescent beads emitting across a wide wavelength spectrum recorded in a dual-arm MFM appended to a commercial microscope with a 100 × NA = 1.45 oil objective (Nikon). Beads were imaged simultaneously in two colors, chosen to match the dyes and fluorescent proteins used in our transcription imaging experiments with orange 590/40 nm and red 676/30 nm emission filters in the respective arms. Pixel size and z-scan step was ≈81 nm to obtain isotropic voxels. Above: PSF of a single fluorescent bead simultaneously measured on the two cameras, with orange and red emission filters in each optical arm respectively. Each z-step was as an average of 4 images before proceeding to the next z-step. Below: Separation distance between each focal plane was measured as an average of 10 beads for each color. Standard deviation of each point is ≈20 nm. Linear regression determined a slope of 407 nm for both orange and red channels with R > 0.99. While the z spacing is the same in the two arms, the focus points are here slightly shifted (≈100 nm) relative to each other thus the points are not overlaid. Scale bar in d represents 1 μm.

Optimal light distribution for nine-plane MFM is obtained by multiplexing an incoming light beam evenly into 3 × 3 diffractive orders with minimal light loss. Grating functions with a larger number of phase steps have better theoretical performance, but each step level makes fabrication of devices more challenging. (a) 32-phase grating function with ≈94% theoretical light efficiency. (b) 16-phase grating function with ≈93% theoretical light efficiency. (c) Eight-phase grating function with ≈89% theoretical light efficiency. (d) 3D perspective plot of the pattern in c to show the steps of the optic (not to scale). (e) Distribution of light into the nine central orders that will form the multifocus image. (f) Bar diagram showing the theoretical relative light intensity distribution of the 3 × 3 center orders in e produced by the device pattern in c and d, expressed in percent of the light intensity of the incoming beam. The zeroth order (i.e. the central image tile, i.e. the nominal focal plane) is intentionally suppressed to compensate for losses in the non-zero orders in the chromatic correction element. Code to generate MFG grating functions like these is included in Code File 1, [].

(a) Grating function of binary MFG for 7-plane MFM with increased image brightness. (b) Diffraction of the pattern in a generates seven diffraction orders with ≈79% total efficiency. Compared to the nine-plane MFM, the first and last image tiles are blank. (c) Signal strength response of each diffractive order in b plotted in a bar diagram. As in the nine-plane system, the zeroth order (central image tile) is intentionally suppressed to compensate for uneven losses in the chromatic correction element. (d) Two 100 nm fluorescent beads mounted in agarose, imaged in the 7-plane MFM with a 150 × glycerin immersion NA = 1.35 objective (Zeiss). Beads are in focus in the nominal focal plane and the gradually decreasing out-of-focus signal can be seen in the other six focal planes. The z-step between successive focal planes in the multifocus image is ≈300 nm. (e) Projection of a focal stack of a single bead shows the diffraction-limited PSF of the MFM system in each image tile. Scale bars in d and e represent 2 μm.

Neuronal signaling in response to odor in C. elegans visualized using the calcium indicator GCaMP6s expressed in sensory neurons. (a) Cartoon of the sensory neuron cluster on the left side of the animal’s head. The right side of the head has a mirror-symmetrical cluster of neurons. (b) MFM image from a movie recorded using the multi-phase MFG, showing the two clusters of sensory neuron pairs on each side of the head. Successive focal planes in the MFM image are separated by 2 μm steps covering a total depth of 18 μm. The lateral field of view in each focal plane image tile is ≈40 × 40 μm². The living animal is immobilized in a microfluidic chamber and imaged during olfactory stimulation with benzaldehyde odor (almond smell). Several neurons can be seen responding to odor stimulation in the movie Visualization 1. Images b and c have been time-averaged since all neurons are not active in a single time-point. Data has been contrast adjusted, background-subtracted and is displayed using an inverse lookup table. Raw data is also provided in Dataset 1, []. (c) View of the cluster of neurons in the focal plane z = + 4 indicated by the blue square in b. (d) Intensity profile plot of the GCaMP6s signal of the neuron indicated by the green oval in c shows an on response to the addition of benzaldehyde odor. (e) Intensity profile plot of the GCaMP6s signal of the neuron indicated by the pink oval in c does not show response to the odor stimulation but has a constant baseline fluorescence level. (f) Intensity profile plot of the background in the region indicated by the blue oval in c, where there are no labeled neurons present. The three intensity plots in d-f are made from equal image areas and displayed in the same scale of arbitrary units (camera pixel counts). Scale bars in b and c represent 10 μm.

Compressed (2^N) lithography masks for fabricating multi-phase MFGs from fused silica (glass) wafers. Multiple etch rounds use the different masks to successively shape the MFG patterns. (a) Multi-phase grating function for nine-plane MFG calculated using the pixelflipper algorithm []. (b) Lithography masks for manufacturing the eight-layer pattern in a, compressed into N = 3 masks (2³ = 8) with active areas that partially overlap during the three successive etch rounds. (c) Multiple solutions to a desired energy distribution are sometimes found during grating function design. For example, this pattern provides an intensity distribution that is effectively identical to that of the pattern in a. By exploring different shapes and different layer orders one can find patterns suited for the manufacturing process. (d) Lithography masks for the pattern in c.

Fabrication process for multi-level MFG devices. Complete code for generating the grating function, separating it into layers and applying the distortion function is available in Code File 1), [], Code File 2), [], Code File 3, [], and Code File 4, [].

(a) Visual inspection of a fused silica (glass) wafer with multiple MFG devices etched into its surface. Each individual device is visible as a lighter circular area on the wafer. (b) Image of MFG surface, showing the pattern / grating function. (c) AFM image of the MFG surface in b. Scale bars in b and c represent 12 μm.

Light efficiency and light distribution uniformity of MFGs measured using an LED light source, filtered by narrowband emission filters (FWHM ≈20 nm at center wavelengths of 438 nm, 485 nm, 513 nm, 585 nm, 632 nm and 660 nm) and a digital single-lens reflex (DSLR) camera sensor (Canon). To ensure a linear response of the camera sensor, it was only used up to < 2/3 of its dynamic range. Transmission losses through the MFG substrate were ignored by comparing to a measured total light value transmitted through a blank part of the device surface. (a) Measured intensity distribution of binary MFG device for 7 focal plane imaging is ≈79% as theoretically predicted. (b) Measured intensity distribution of eight-level multi-phase MFG device for 9 focal plane imaging is lower than the ≈89% theoretically calculated, varying between ≈74% and 84% in fabricated devices from different batches. Note that the intensity of the zeroth diffraction order (the central image plane in the multifocus image) is intentionally suppressed in the MFGs in both a and b to compensate for uneven losses in the chromatic correction module. Uniformity between orders is a sensitive part of the grating function design and fabrication process, and especially the relative intensity of the zeroth order varies strongly with the effective phase shift for different wavelengths. Measurement accuracy and device uniformity was estimated jointly by inspecting three MFGs from the same batch, yielding a standard deviation of 0.3%. (Total efficiency in n = 3 measured devices in this batch averaged 79.0% with standard deviation 0.3% at the design wavelength ≈513 nm.) Measurement accuracy was also confirmed for a subset of devices with an optical power meter, yielding values consistent with the measurements made with the camera sensor within a few percent.