Dual color DMD-SIM by temperature-controlled laser wavelength matching: supplement

Structured illumination microscopy (SIM) is a fast and gentle super-resolution fluorescence imaging technique, featuring live-cell compatible excitation light levels and high imaging speeds. To achieve SIM, spatial modulation of the fluorescence excitation light is employed. This is typically achieved by interfering coherent laser beams in the sample plane, which are often created by spatial light modulators (SLMs). Digital micromirror devices (DMDs) are a form of SLMs with certain advantages, such as high speed, low cost and wide availability, which present certain hurdles in their implementation, mainly the blazed grating effect caused by the jagged surface structure of the tilted mirrors. Recent works have studied this effect through modelling, simulations and experiments, and laid out possible implementations of multi-color SIM imaging based on DMDs. Here, we present an implementation of a dual-color DMD based SIM microscope using temperature-controlled wavelength matching. By carefully controlling the output wavelength of a diode laser by temperature, we can tune two laser wavelengths in such a way that no opto-mechanical realignment of the SIM setup is necessary when switching between both wavelengths. This reduces system complexity and increases imaging speed. With measurements on nano-bead reference samples, as well as the actin skeleton and membrane of fixed U2OS cells, we demonstrate the capabilities of the setup.

: Diffraction order intensities in the Fourier plane Average and maximum normalized diffraction order intensities in the Fourier plane at 473 nm (upper half) and 631 nm (lower half) measured in a circle with 30 pixels / 0.05° diameter around the diffraction maxima. The symmetrical intensity distribution of the diffraction order in both channels with deviations of less than 9% in the average and 15% in the maximum can be a good quality feature for the correct angle of incidence (blaze angle) of 43.7° on the DMD. Simulated with 350×350 individual mirrors, with a grating constant of = 7.56 µ , a tilt angle of = 12° and an incidence angle of = 43.7° ( = -= 34.05°) . The measured and simulated diffraction images are integrated over the three SIM angles and were formed using the SIM patterns intended for the 631 nm channel. For this reason, the intensity of the central diffraction order is higher by a factor of three than it would be for a single SIM angle. The position of the first side orders do not overlap because the pattern of the 631 nm channel was used for both channels. As a result, the first side orders of the 473 nm channel are closer to the central diffraction order. (I-III) Cross-section plots (10 pixels / 0.017° wide) through the measured (black) and simulated (green) diffraction maxima in the Fourier plane. For SIM angles I and II, the measurements and simulations agree very well. SIM angle III deviates slightly from the simulations in the measurement. We see non-linearities in the diffraction/angle space of the simulations as the reason for this. These increase along the diagonals as soon as the small angle approximation is no longer fulfilled ( = -19.7°) . SIM angle III is oriented almost identically to the diagonal.    4). The inlays each show the magnification of the central diffraction order. The yellow crosses in the center serve as a static reference to the moving central diffraction order. With increasing temperature and wavelength, all diffraction orders migrate along the diagonal perpendicular to the tilting axis of the DMD's micromirrors. Several mode jumps with a distance of approx. 82 µm can be seen on the camera chip. This is equivalent to an angular difference of approx. Δ = 0.02°, which in a linear approximation of the native grating diffraction of the DMD corresponds to a mode jump of approx. Δ = 0.5 each. This is about twice the mode jumps described in the data sheet of the laser diode. We assume that in our case we can only observe double mode jumps, since the modes in between either hardly oscillate or smaller temperature steps are required to see them. In (f) it is easy to see that sometimes even three modes can be active at the same time. For operation as a SIM microscope, it is desirable that only one mode is active, as can be seen in Fig. 5 (main manuscript).  Figure S5). The cyan circles outline where the Fourier filter mask, which needs to be used to block spurious diffractions caused by the binary structure of the DMD, is opened to allow for the 1 st diffraction orders of all SIM angles to pass through to the objective. This visualizes that precise wavelength matching, down to about 1°C in case temperature, is required. If the wavelength mismatch is larger, the Fourier pattern shifts so much that the SIM pattern can no longer pass through the filter mask. Vis versa, this effect could be used as a feedback mechanism to find the correct case temperature, as is basically replicated the function of a spectrometer.

Red laser diode wavelength and mode-hopping:
The AlGaInP laser diode (Ushio, HL63163DG) has a typical wavelength of 633 nm with 100 mW output power at 170 mA operating current (single transvers spatial mode).
The wavelength (longitudinal mode) of the laser diode depends on the temperature of the laser diode (approx. 0.2 nm/°C) and on the injection current (approx. 0.05 nm/mA). With fixed current the wavelength of the laser diode can be altered by changing the temperature.
With raising temperature, the refractive index and the length of the laser cavity, and therefore the wavelength, increases. If the (longitudinal) mode no longer fits into the cavity a neighboring mode oscillates. This course a mode jump of about 0.2.5 nm which can be seen in the curves (see Figure 3b, main manuscript). These mode hops are not reproducible (temperature dependent hysteresis). Sometimes the laser diode is running in two or more longitudinal modes as can be seen in Figure 8 (main manuscript).
The laser diode (5.6 mm TO Package) is mounted on an external thermo electric cooling element for controlling the diode temperature together with a thermistor for measuring the case temperature. All parts are in a round housing which fits in the 30 mm cage system (Thorlabs). With the laser diode controller (Meos LDC-01) it is possible to set the temperature in steps of 0.2°C, over a range of 5 to 40°C.
The strongly divergent laser beam is collimated by a aspheric lens (f=9.6 mm, NA=0.3, Thorlabs C060TMD-A) The collimated beam with its elliptic shape than is coupled into the single mode fiber with a further aspheric lens (f=15.29, NA=0.16, Thorlabs C260TMD-A).

Two dichroic mirrors from the same batch
The DMD SIM setup uses a combination of two dichroic mirrors, reflecting in a horizontal and vertical arrangement. This is a typical solution to realize a SIM setup with off-the-shelf dichroic mirrors, as it solved the problem of polarization-dependent phase delay. With a standard dielectric mirror [5], the P-and S-polarized components of light being reflected exhibit different amounts of phase delay. In many applications, this does not cause issues, as either maintaining polarization is not of importance, or light is purely P-or S-polarized (often the case when using fully horizontally or vertically polarized light and reflecting it in the same plane on an optical table). However, in SIM, different polarizations that do not align with P-and S-polarization of the mirror have to be maintained to obtain full pattern contrast in the sample plane, while the different phase delays cause the polarization to become elliptical [6].
An easy solution that does not require custom components is using two dichroic mirrors in an arrangement as described above, so that light that is S-polarized for the first mirrors is seen as P-polarized by the second mirror, and vice versa. Thus, the different phase delay effects cancel out, and the delay becomes independent of polarization state. For this to work, we have found that two completely identical mirrors, ideally produced in the same batch, should be used.
As an additional remark, all conventional mirrors should be checked for polarization effects when they are used in a SIM excitation path. However, when no dichroic properties are needed, using metallic instead of dielectric mirrors typically provides an easy solution to achieve a polarization-maintaining light path.

Slightly elliptical polarization after the DMD
The polarization of the excitation lasers from the DMD is S-polarized. We have noticed that the polarization behind the DMD is no longer exactly s-polarized, but slightly elliptical. Presumably, this effect is caused by the protective glass in front of the DMD. To get around the problem, we placed a linear polarization filter behind the DMD.