When I print the camera view to a jpg file, the file size is about 650k. I would like to have a much higher resolution picture, with a file size of at least 3MB.
How do I do that?
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What you are referencing "650k" and "3MB" is the file size, not the image resolution. While an increase in resolution likely increases the file size, it actually depends on the image format and its encoding/compression. A very high resolution image can be small in file size with a good compression algorithm.
When talking about image resolution this typically means the number of pixels stored in the images, which is commonly written as the number of pixel on the horizontal axis (X-axis) times the number of pixels on the vertical axis (Y-axis), e.g. 1920x1080. This resolution can be adjusted in the Output tab in Blender.
If for some reason you really need to create image files with a certain file size, then I'd suggest using a file format without compression which lets you estimate the resulting file size based on the resolution and the overhead from the header, trailer and additional metadata of the file format.