Active Microscope Stabilization in Three Dimensions Using Image Correlation.

3D drift tracking by image correlation

As with many other techniques to measure image drift, we employ cross-correlations using fast Fourier transforms. Cross-correlating two images yields an equally-sized image with a maximum whose position depends on the relative shift between the two images and whose intensity depends on their likeness. By tracking the peak position of the correlation function, we can determine the xy drift in the image plane. Here, we extend the practice of image correlation to also monitor out-of-plane drift. Defocusing caused by z drift perpendicular to the image plane results in a decrease in the peak height of the correlation function. Nevertheless, this decrease by itself does not indicate the direction of the drift (positive or negative z ). Therefore, we correlate the image with an image taken above the focal plane and another image taken below the focal plane. An upward sample drift will lead to an increase in the peak value of the first correlation and a corresponding decrease of the second, whereas a downward drift will have the opposite effect. The difference of these two peak values then uniquely determines the amount and direction of z drift. In practice, before data acquisition begins, we record three reference bright-field images at, below and above the focal plane (denoted as I 0 , I − , and I + , respectively, Figure 1 ). The in-focus and out-of-focus images are separated by a z distance of d . During data acquisition, bright-field images are simultaneously captured, with the n th frame denoted as I n . For convenience, we represent the correlation function of two images I a and I b as (1) C a , b = ∫ ∫ I a ( x , y ) I b ( x − x ′ , y − y ′ ) d x ′ d y ′ = ℑ − 1 { ℑ ( I a ) ℑ ∗ ( I b ) } . For each new bright-field image acquired, I n , three correlation functions are calculated: with the in-focus reference I 0 and with each out-of-focus reference I − and I + . The resulted correlation functions, C −, n , C 0, n and C +, n are then each fit to a 2D Gaussian function in a 20-by-20 pixel window to find both the peak value, PV , and peak position, PX and PY . The x and y drift can be derived from the in-focus correlation: (2) Δ x = P X { C 0 , n } (3) Δ y = P Y { C 0 , n } When the z drift is small, it can be approximated by a linear combination of the two out-of-focus correlations: (4) Δ z = α ( ζ n − ζ 0 ) with (5) ζ n = ( P V { C + , n } − P V { C − , n } ) ∕ P V { C 0 , n } The coefficient α can be measured from the three reference images: (6) α = ( 2 × P V { C 0 , 0 } − P V { C + , 0 } − P V { C − , 0 } ) ∕ 2 d Optical setup Our super-resolution microscope, as described previously ( Mennella et al. 2012 ) is custom-built from a Nikon Eclipse Ti-E inverted microscope. The microscope is placed on a vibration isolation table (ST-UT2, Newport) in an optics room without special temperature control and located on the 3rd floor of a building. We equipped the microscope with a piezo z stage (Nano-Z100, Mad City Labs) mounted on a motorized xy stage with a step resolution of 10 nm (SCAN IM 120×100, Märzhauser). Four lasers (405 nm, 488 nm and 642 nm, Vortran Lasers, and 561 nm, Sapphire 561–200, Coherent) were combined and focused to the back focal plane of the objective (Nikon 100× Plan Apo VC NA 1.4) for activation and imaging. A dichroic mirror (zt405/488/561/640rpc, Chroma or T660lpxr, Chroma) and an appropriate band-pass filter (ET702/75m, Chroma, for fluorescence emission of Alexa Fluor 647) ensure the separation of the excitation light and the fluorescence emission. A cylindrical lens (700 mm focal length) is inserted between the microscope body and the image plane at the side port to create astigmatic aberration that allows 3D single-particle localization and 3D super-resolution microscopy ( Huang et al. 2008b ). Super-resolution images are recorded with an electron multiplying CCD camera (EMCCD, iXon+ DU897E-C20-BV, Andor) using a custom-written software in Python. To incorporate our new drift correction scheme, we have made the following modifications ( Figure 2 ): an IR LED (850nm; M850L2, Thorlabs) to replace the trans-illumination halogen lamp for bright-field imaging, a short-pass filter in front of the EMCCD to block the IR light (ET750SP-2p, Chroma), a dichroic mirror (765dcspxr, Chroma) to direct the IR light collected by the objective through a band-pass filter (HQ850/90x, Chroma), and a 75 mm lens to image the IR light on an inexpensive CCD camera (DMK 31AU03, The Imaging Source). The IR wavelength was chosen so that it is long enough to avoid overlap with photoactivation or fluorescence emission wavelengths, and short enough for ordinary silicon-based CCD or CMOS cameras to have sufficient sensitivity. We used a custom-written program in Python to collect and analyze the IR images in real time. The program controls the piezo z stage and the motorized xy stage to actively compensate the drift of the sample.

Sample Preparation and Imaging

We have used our microscope to stabilize two different samples: fixed Drosophila S2 cells grown on a coverglass-bottom petri dish, and dissected, fixed Drosophila embryo sandwiched between a glass slide and a piece of coverglass. To evaluate the performance of our focus stabilization system, we added 100-nm-diameter TetraSpec fluorescent beads (Invitrogen) to the sample and allowed the beads to adsorb to the coverglass surface. Facilitated by the cylindrical lens, we tracked the 3D positions of these beads using the EMCCD camera, and measured the stage drift by averaging the movement of multiple beads. Using STORM and our drift correction method we imaged Drosophila embryos expressing GFP∷Cdc42 in the aCC/RP2 motoneurons stained as described previously ( Kamiyama and Chiba 2009 ). Briefly, the embryos were fillet-dissected, fixed with 4% paraformaldehyde for 10 min, and stained by anti-GFP antibody (Invitrogen) on a glass slide. Following incubation with the anti-rabbit secondary antibodies conjugated with Alexa Fluor 405 and Alexa Fluor 647 (Invitrogen) for 2 hours, they were post-fixed with 4% paraformaldehyde for 5 min. To increase the refractive index of the mounting media we used a solution of 80% 2-2' Thiodiethanol (TDE) along with 100mM mercaptoethylamine at pH 8.0, 5% glucose (wt/vol) and oxygen scavenging enzymes (0.5 mg/ml glucose oxidase (G2133, Sigma-Aldrich) and 40 μg/ml catalase (C30, Sigma-Aldrich)).