APh 162 Week 1 Day 1 Objectives: • Optical resolution • Light path of the microscope • Kohler illumination • Lens aberrations The microscope has been central to the practice of biophysics or physical biology. Beyond needing lenses of some sort to document phenomena, we use microscopes to look at stuff that is smaller than what we can resolve with our own eyes. Thus, an understanding of resolution is critical to choosing what sort of microscope we would like to us e. Additionally, in this lab we will get used to using the microscopes. Though the number of exercises is small, it will still take a bit of time as you learn how to set up microscopes (Micromanager), acquire data, etc. Lab 1 – Getting to know your microscope Brightfield microscopy. Undoubtedly, in the coming weeks, there will be times where the microscope seems to be not “working.” A good way to diagnose an overly dark image, or a non‐uniformly illuminated sample, or trouble‐shooting in general, is to think about what’s going on in the lightpath. The diagram on the left displays the brightfield illumination pathway of the microscope. What is constant between all the brightfield techniques we will be dealing with is the use of Koehler illumination. Koehler illumination means that the sample is illuminated uniformly, so any structure or hot spots in the lamp filament will be minimized; as well, in Koehler, the full numerical aperture of the condenser lens is utilized, which boosts the resolution of the microscope (see below). 1. Identify the brightfield pathway of one of the microscopes with your TA. 2. Align the microscope in Koehler. 3. Become familiar with Micromanager, which runs most ate how sharp the edges are using a 10‐90% . What happens to the image? One of the 60x objectives also has a variable numerical aperture. of the microscopes in the lab. 4. Edge‐based resolution test: get one of the targets that has small bars on it. These targets ha ve edges that have sub‐wavelength sharpness. Estimcriterion. How does this match ideal resolution? 5. Depth of field: Find a sample that has some depth to it. Now stop down the condenser apertureWhat happens to the image if you reduce the NA of this lens, keeping the condenser aperture size constant? 6. Become familiar with the fluorescence light path. 7. Get a solution of fluorescent beads that have diameter greater than the resolution minimum. Estimate the resolution from an image of a bead. Is this the size you expect (i.e., compare the size to the manufacturer specifications)? If there are any discrepancies, please explain. 8. Point‐spread function: We can characterize the optical response of a microscope by its “point‐spread function”. Basically, the PSF tells us how the microscope images a point object. The PSF is a 3 dimensional object. Get some diffraction‐limited fluorescent beads and take a z‐stack of the beads. Reconstruct the PSF in 3D. Why is there out‐of‐focus light? What are the limits of resolution in x, y, and z? Lab 2 ‐ Fourier Optics In this set up, we have “blown up” a conv entional microscope to reveal its innards. With this, we will be able to visualize the 2D Fourier transform of some objects, and to understand what a microscope is doing. By blocking or passing some of the Fourier components, you will be able to modify the characteristics of the resulting image. Below is a simplified diagram of the instrument: A laser beam, collimated by the condenser lens, illuminates (red arrows) a transparency placed at the object plane, one focal length distance from the objective (f2). Light is diffracted (green arrows) off the object which has the electric field distribution E0(x,y) and is collected by the objective. An image of the object is formed by the tube lens, which interferes the light at its focus (f4). The same principle holds for imaging the Fourier transform of the object: the Fourier transform (with electric field distribution EFT(x,y)) appears behind the objective at the Fourier plane, or back focal plane. X and Y are the spatial coordinates of the Fourier plane. We subs equently image the Fourier transform (blue arrows) on the Fourier plane (camera 2). Objects in real space (x) are transformed according to X/fλ, where f is the focal length of the objective (200 mm), and λ the wavelength of light (660 nm). The dimensions of the Fourie r transform are hence m‐1. We will illustrate with a few samples. Note that we are actually observing the intensity of light at the Fourier plane, that is, the magnitude of the Fourier transform, and not the actual transform itself. We are actually measuring the power spectrum of the object, or, how much optical power is within each spatial frequency of the object: 1. Identify the components of the “microscope” with your TA. How does the spatial filter work, given your knowledge about diffraction? 2. (not required) What is the magnification of the system (optical and digital)? Knowing this, calibrate the camera on the tel evision screen(s). What do you suppose the smallest object you can see is? How does this compare with dmin (see below)? 3. Use a grating pattern in the object plane. Do the Fourier space coordinates match the spatial frequency seen at the image plane? Use both a high frequen cy and a low frequency grating. Please describe the measured results. What is the central spot? Why is it always there? 4. (not required) Use a grating pattern with symmetry in more than one direction. Does the power spectrum make sense? What happens if you rotate the object? What about a grating with variable line density? 5. (not required) Use the various patterns; see if you can predict its Fourier transform! 6. Place a mask in the path of the Fourier space to filter the Fourier transform. What happens if you use a high frequency grating and block off the Fourier components furthest from the center? How does this relate to resolution? Now we know that an object with spatial extent d placed one focal length away from the objective has as its transform components which are approximatel y 1/d in Fourier space. Thus as the object becomes smaller, the Fourier component moves further and further from the origin. However, a lens is only of finite diameter, and cannot therefore capture all Fourier components of a diffracted object. The objective of a microscope, which serves to collect the light diffracted by an object, thus serves as