Opportunity is missed by most people because it is dressed in overalls and looks like work. - Thomas Edison
Though I don't know what kind of file you're starting with, that logo would be fine as a bitmap tif. No grays, just black and white. If it's a raster image, it starts with that file's physical size and resolution. I might take a decent sized jpeg into PS and run it through PhotoZoom Pro to enlarge it and smooth the edges. I usually go up 2X. Then, I'll open the resulting image in PS, and increase the resolution to at least 600 ppi. Then, some judicious Gaussian Blur, as little as possible, just to the point where the image looks smoother, then go into Curves and drag the top and bottom points close to the 50% mark, but don't cross the line. This will give some smoother hard edges, hopefully. Then, take it through the modes in the Image menu to Bitmap (if your original is CMYK or RGB, you have to make it Grayscale first). The last step is to reduce it to the final size, which makes it even a little less noticeable. I've fixed a lot of sponsor logos with this trick, though it's useless with tiny images. For this particular image though, why not just redraw it with vectors?Steve
I use threshold on literally ever spot color film out of photoshop. Even if you import a vector black image at super high DPI it will have subtle gray/translucent pixels on the edges due to the raster vs vector.