Use Snell’s law to determine the angle of total internal reflection in the coverslip (without oil). Oil immersion objectives More light (no total internal reflection at coverslip) More diffraction orders from sample (smaller Airy pattern will result) Oil shortens the wavelength of the light so d min decreases (this only works if light never enters air). Murphy 2001

In terms of fundamentals of optics, for 2 points to be resolved, the max. of one object’s diffraction pattern must overlap the 1 st min. of the other. This is called the Raleigh/Abbe criterion. In terms of instrumental sampling, we want 2 pixels to fit in the linear dimension of each pattern (4 pixels/area). Here we are matching our optical resolution to our instrumental resolution. This is called the Nyquist criterion. How can oversampling be a problem? Assuming the 1 micron dimension is correct, what is the size of each pixel? What do we mean by sampling? undersampledproperly sampled ~1 micron (for a good oil objective) 500 um When sampling with more pixels, adjust scan rate to increase photons/pixel; this is a good idea unless you are worried about beam damage! The top row of 3 scans (not in box) was done at constant scan rate (what is the scan rate for the top row?) The photon flux from the sample in all cases is 16 photons/second. Adapted from Pawley 2004 This 500um scan range can be mapped to ??? pixels. The scan itself can be other than 1:1 aspect ratio but the pixels are each 1:1. d min =1.22 λ / 2NA fast (? sec/scan)slow (4 sec/scan)Slowest (? sec/scan) The Bio-Rad MRC1024 (when not set to low signal) automatically corrects for changes in scan rate by decreasing PMT (photomultiplier tube) output at slower scan rates. With low signal turned on, collect images at slow and normal scan rates (what are these rates in lines/sec)? How does this value relate to temporal (time) resolution? These represent light from the object as it is focused at the image plane. They are not points! ~1 micron (for a good oil objective)

Axial or z resolution: z min = 2 λ air η sample / (NA obj ) 2 DON’T MEMORIZE University of Helsinki y x z y or x When doing 3D confocal microscopy, we want to match our corrected z-step with the proper sampling depth of our setup. It also helps some reconstruction programs if we can make our xy:z aspect ratio an interger value. Adjust scan size, z step, scan rate, and pixel count to match your objective lens and sample. Now, image the same sample with each of the above parameters set to non- optimal settings. This is ultimate z resolution, how does our z resolution change with confocal iris size?

During z-series acquisition the distance in z axis travel by the objective or sample is different than the change in z of the focal plane. The next 3 slides show why it is necessary to use a z- correction factor when collecting stacks of optical sections (z-series).

20X NA / um given 190 um given (you can start at any focal distance you want to, just turn the focus knob) 119um 90um Extreme ray angle (degrees) 45 air, 28 glass, 32 water 20X NA /.17 WD air WD water with coverslip α 1 α 2 When you turn the focus knob and move the objective 10um closer to the sample what is the change in plane of focus in the sample? Often, the WD printed on the objective actually is a measure of the distance between the objective front lens and the coverslip. α 1 microscope tube length coverslip thickness, 170um

20X NA / um 206 um (now we’ve moved the focus knob (objective) 10 microns closer to our sample) 129 um 90um 10um Extreme ray angle (degrees) 45 air, 28 glass, 32 water α 1 α 2 10um We use peripheral rays for correction factor. (Visser & N.S. White use modal rays, see ref. at end)

Gaussian z depth correction factor for z series reconstruction NA = (refractive index of medium at lens) η x sin α Nominal z-step = 10 um Actual z-step = 16um Nominal z-step/correction factor = optical z-step Correction factor =.63 (also.63 when simple equation used: η1 x cosα 1 / η2 x cosα 2 ) Coversilp determines absolute focal depth but has no effect on focal shift with change in focal depth because its thickness is constant while the depth into sample is not. As described in Zill, Microscopy Research and Technique Volume 48 Issue 6Volume 48 Issue 6, Pages Based on work of Nick White.

Be aware of spectral bleed through or leakage; picking up the same emissions in 2 or more channels. This can appear to be co-localization when it is not. invitrogen.molecular.spectra.viewer