Two-channel device

The two-channel wedge device deflects light toward the centers of the two CCD halves and consists of two identical custom-made semicircular wedges paired with semicircular filters. For each wedge, we ground down a blank 25 mm-diameter, 5 mm-thick BK7 window at a wedge angle of 1.24° to the axis. We confirmed the angle using a digital micrometer in conjunction with autocollimation. We polished the circular wedge faces to a flatness of better than λ/4 @ 633&#;nm. Employing an autocollimator we positioned the circular wedge and cut orthogonal to the gradient to create the semicircular wedges. The device&#;s filters originated from Chroma Technologies. We cut off-the-shelf 25 mm-diameter emission filters (red ET632-60&#;m and green ET520-40&#;m) through their center to generate the semicircular filters. We assembled the parts using rapid-curing epoxy to create the prototype. The filter cube also contained excitation and dichroic filters from multichannel filter set .

View Details

Figure 3a shows an image of the custom two-channel wedge device in the emission filter position of the filter cube, while Fig. 3b shows a representative false-color image of C. elegans PLM neurons expressing green GCaMP and red mCherry genetically-encoded fluorophores. We characterized this device by imaging fluorescent beads and thin films of fluorescent dye (see Methods). While each channel of our device only uses 50% of the available light, under some objectives, the total transmission through a microscope with our two-channel device can be comparable to the total transmission through a microscope with a dual-view instrument. As shown in Table 1, the transmission with the two-channel wedge device, Twedge, is 57&#;96% of the transmission with a dual-view instrument, depending on the objective used. We attribute this lower than expected loss to the fewer optics producing back reflection and absorption in the wedge device compared to a dual-view instrument. Testing confirms an image displacement that matches the theoretical prediction (see Table 1). As further described in the Methods, we registered images by eye or a cross-correlation program and extracted horizontal and vertical translation parameters for use in future imaging. To orient the deflection direction along the long dimension of the camera array we manually adjusted the azimuthal angle of the entire device (rotating in the mount) by eye. Even so, the custom wedge device tiles the channels on the camera sensor very effectively, with only 3.8% of the sensor area not represented in both channels. Assuming a well-aligned microscope, precision alignment under mass production should eliminate the need for user alignment and further improve the performance.

Figure 3

Wedge devices and testing. (a) Two-channel device installed in filter cube. (b) Two-channel false-color image of C. elegans neurons in vivo. (c) Four-channel device in emission filter housing. (d) Four-channel false-color image of red and blue-green beads. Red boxes outline channels. Lower left channel includes red, green, and blue light. (e) Diagram of green fluorescent bead PSF measurement without and with wedge device. (f&#;h) Resolution measurements under various objectives without (dashed) and with (solid) wedge device. FWHM values of PSF extent in x (yellow), y (blue), and z (green) are dependent on bead x position. Each point is the average of data from 40 beads. PSF FWHM from simulations indicated as points. Insets show simulated transverse PSF heatmaps at corresponding points.

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We also characterized changes in imaging resolution from the addition of our wedge device to the microscope imaging beampath. Following established procedures3 we acquired 3D image stacks (i.e., z-stacks) of sub-diffraction limit 175-nm green fluorescent beads with and without our wedge device, and we utilized the PSFj software package3 to calculate the full width half maximum (FWHM) values of the point spread function (PSF), which we abbreviate as PSFxyz below. The typical PSF for an ideal objective in a well-aligned microscope is isotropic in the lateral (xy) plane (see Fig. 3e, left side) and does not strongly depend on position in the image. The objectives and system demonstrate roughly ideal performance (see Fig. 3f&#;h, dashed lines).

The wedge deflects the center portion of the original FOV (see Fig. 3e, left) to the two halves of the CCD (see Fig. 3e, right). We measured the PSF on the left half of the CCD with green fluorescence. The PSFy with the wedge (solid blue line) closely tracks the PSFxy without the wedge (dashed blue line). The PSFx exhibits some interesting features upon introduction of the wedge device (see Fig. 3f&#;h, solid lines). The two most salient features are an increase in PSFx compared to PSFy and a dependence on the x position (direction orthogonal to the wedge interface). First, when utilizing the wedge device, the PSFx for all points is significantly greater than the PSFy. As described above, this overall increase is likely due to chromatic aberration. In the direction of the wedge deflection, x, the wavelengths are spread out due to a wavelength-dependent index, increasing the PSFx from the diffraction-limited minimum width, which is approximately PSFy. By dividing the green BK7 lateral shift in Table 2 by the magnification, we can obtain a rough upper bound on the increase: 1.25, 0.62, and 0.21 μm for 10, 20, and 60x, respectively. The measured increase (approximately PSFx &#; PSFy of beads near the left side of the FOV) is about 50&#;70% of our upper bound. The beads utilized have a peaked spectrum within the filter bandwidth, reducing the wavelength range and the increase from the diffraction limit. Second, both the PSFx and PSFz increase significantly as the position approaches the CCD center. Qualitatively, this increase in PSFxz occurs because the effective numerical aperture of points imaged near the CCD center is reduced compared to points imaged near the CCD edges: As shown in Fig. 1d, the objective is a converging lens and refracts light originating from one side of the sample toward the contralateral side. Our device is beyond the objective back focal plane, so light originating from one side of the sample primarily transmits through the contralateral wedge and filter. In Fig. 1d, the beam of light originating from the object arrowhead primarily passes through the green filter and wedge underneath. Depending on the objective parameters, a smaller portion of the beam passes through the red filter and wedge. The opposite is true for the light beam originating from the object base (not shown). This dependence of beam size on position yields an effective decrease in the numerical aperture for points imaged near the CCD center (light originating from same side as wedge) compared to points imaged near the CCD edge (light originating from side contralateral to wedge). The beam extent and, hence, the numerical aperture in the x direction decreases, but the beam extent and the numerical aperture in the y direction does not decrease. Thus PSFx and PSFz increase, but PSFy is roughly unchanged for points near the CCD center. We are currently quantifying the effect of various objective parameters, such as the numerical aperture and back aperture, on the PSF.

We simulated the effect of our wedges on resolution and aberration in our microscope using the Huygens calculation in Zemax. We obtained the transverse PSF of the microscope system with wedges at five locations in the FOV. As shown by the data points in Fig. 3f&#;h, the simulated and experimental PSFy match closely. The computed PSFx follow the trends seen experimentally. The intrinsic functions in Zemax are not conducive to straightforward PSFz computations. Computed PSFz (data not shown) were significantly greater than most experimental PSFz, and the trends across the FOV were less pronounced. We believe the experimental PSFz is a better measure of the performance of our device.

We obtained Seidel coefficients from Zemax (see Supp. Table S1) which indicate that the aberrations from the front surface of the wedge (surface 9) are cancelled by the back surface of the wedge (surface 10). Both measured and calculated PSFs (see Fig. S2) also show minimal secondary peaks that are the hallmarks of aberration4. Thus, wedges introduce negligible spherical aberration, coma, astigmatism, field curvature, and distortion.

Four-channel device

A distinct advantage of the wedge approach is easy scalability to a greater number of channels. The four-channel device deflects light toward the four CCD quadrant centers by defining two wedge parameters: a single altitudinal wedge angle set by the distance from the CCD center to the quadrant centers and an azimuthal angle set by the deflection angle to each quadrant center. The FOV of each channel is one quarter of the original FOV with no change in magnification. Each channel utilizes 25% of the available light. We fabricated the four-channel device (see Fig. 3c) by machining a BK7 window at a wedge angle of 1.55°. We quartered the circular wedge at an azimuthal angle of 0&#;±&#;36.8° or 180&#;±&#;36.8° to the wedge gradient to create wedge quadrants, similar to the two-channel procedure described above. We paired each quartered wedge with a quartered filter (red ET610/40&#;m, green ET530/20&#;m, blue ET470/24&#;m, and all three colors &#;m) specific for imaging Brainbow, a multi-fluorescent protein technique (see below). The filter cube also contained excitation and dichroic filters from multichannel filter set . All filters originated from Chroma Technologies. We adjusted the azimuthal orientation of the entire device by eye. The four-channel wedge device tiles the channels on the CCD well (see Fig. 3d), with less than 14% of the CCD area not represented in all channels. Again, precision alignment under mass production should significantly improve the performance.

Demonstration on animals in vivo and fixed cell sections

We used the two-channel device to measure in vivo intracellular calcium dynamics in multiple neurons of the nematode C. elegans. These neurons co-express baseline red fluorescent protein (RFP) and calcium-sensitive green GCaMP3. The green/red fluorescence ratio (R) specifies the relative changes in calcium levels resulting from neuronal activity or membrane poration. Figure 4a shows a single frame capture of a single axon in an intact adult animal. Figure 4b shows intracellular calcium dynamics at positions 1&#;3. Using a femtosecond laser, we ablated a submicrometer region of the axon at the position noted by the arrow5. Previous studies indicate that laser disruption of the cell membrane allows a large calcium influx into the cell and initiates an intracellular calcium wave from the damage point6. Accordingly, after surgery and transient laser artifact at t&#;=&#;2&#;s, we observe calcium levels rapidly increase as extracellular calcium enters via the surgery site. We note a propagating calcium wave whose onset and height vary with distance from the surgery site. Our prototype device observes excellent fluorescence signal and dynamic ranges (400% change from initial value, R0) similar to those seen by conventional two-channel imaging instruments6.

Figure 4

Demonstration of approach in vivo and in fixed samples. (a) Single frame (0.2&#;s exposure) capture of RFP (red) and GCaMP (calcium-sensitive green) channel images of D-type motor axon in C. elegans in vivo prior to surgery at arrow (out of focus in frame). (b) Relative changes in green/red ratio reveal intracellular calcium dynamics at positions 1&#;3. Laser axotomy occurs at t&#;=&#;2&#;s. Note delay and reduction in calcium transient with distance from surgery position. (c) Recombined image of electroporated chick embryo expressing Brainbow. Each neuron can be distinguished by a cell-specific ratio of fluorophores and intensity (normalized values).

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We demonstrated our four-channel device on Brainbow samples, where neurons express a cell-specific ratio of three or more fluorescent proteins, allowing cell-specific identification of neurons and their fibers by their distinct color7. Brainbow imaging is typically performed by serial fluorophore excitation, often by laser scanning. This leads to differential photobleaching and extensive spectral distortion that necessitates extensive compensatory post-processing. We demonstrated the four-channel device on fixed sections of electroporated chick spinal cords expressing tdTomato (red), yellow fluorescent protein (yellow-green), and mCerulean (blue) fluorophores. Following a minimal registration and post-processing protocol described in the Methods, we successfully identified neurons individually by their spectra and intensity as shown in Fig. 4c. Thus, the four-channel device permits rapid, simple, and robust Brainbow imaging that does not require extensive post-processing.

Optical prisms (wedge prisms) for measuring stand basal area ©

The optical properties of wedge shaped prisms are particularly suited to angle count sampling, and since the early s, the OPTICAL WEDGE or WEDGE PRISM has been used extensively as an angle gauge for basal area estimates.

The prism is a wedge shaped piece of glass which refracts light rays, thus establishing a critical angle. A tree viewed through the prism is displaced through an angle depending on the DIOPTRE STRENGTH of the prism:

One prism dioptre is equivalent to the right angle displacement of an object by 1 unit per 100 units of distance.

In sweeping an area, each tree is counted whose lateral displacement of the image is less than its d (DBHOB).

The wedge prism has two major advantages over instruments like the relaskop :

• only TWO lines have to be aligned
• slight movement of the tree or instrument does not interfere with the alignment: the tree and its image remain in the same relative position.

Thus, the wedge prism is sometimes claimed to be faster and more accurate than the Spiegel Relaskop. In dense stands however, some problems may be experienced in matching the image to the tree! This problem can be overcome by turning the prism through 90 degrees which causes each image to 'return' to the tree from which it derives.

Calibrated wedge prisms can be purchased for $35 to $45.

Effect of Slope on Estimates of G (Wedge Prisms)

To reduce the standing basal area estimate to a horizontal area equivalent, a correction must be made for slope. This is done by multiplying the basal area estimate by Sec Q, where Q is the maximum angle of slope at the angle count spot. Slope can be corrected for in other ways (Barrett and Nevers, ) but all have the same result. The method outlined above is the one generally recommended.

Correction can be ignored for slopes less than 5 as the error is less than 0.5%

         Slope   Secant    Error (%)
           1     1.000     0.0
           2     1.000     0.0
           3     1.001     0.1
           4     1.002     0.2
           5     1.004     0.4
           6     1.005     0.5
           7     1.008     0.8
           8     1.010     1.0
           9     1.012     1.2
          10     1.015     1.5
          15     1.035     3.5
          20     1.064     6.4
          25     1.103    10.3
          30     1.155    15.5

Document URLhttp://online.anu.edu.au/Forestry/mensuration/PRISMS.HTM Editor Cris Brack © Last Modified DateFri, 9 Feb