Trying to understand effect of lens lp/mm on image pixels

There are a number of intricacies here which would take hours to get into. Here are a few quick answers:

First, define the % contrast at which you are specifying the MTF. The value "145lp/mm" should be specified with a percentage, such as MTF of 20%@145lp/mm. Most people use 10-30% image contrast as the minimum resolvable value. This is subjective for visual applications and is based on what is 'good enough' for edge detection algorithms.

If I replace lens #1 with lens #2 and take a picture again, what would the image look like? Would columns 2 and 3 just combine into one column of black pixels? Or is it something more like instead of column 6 being a black line, columns 5,6, and 7 would turn a gray color?

The output will be a defocused gray. This gray will vary in intensity because it is a convolution of scene luminance and lens' optical transfer function. The fourier math is complicated so I won't get into it here. It is typically taught in the 2nd-3rd year wave-based optics courses at the UofA / UofR.

I see lens documentations giving a center resolution and a corner resolution. I always see the corner resolution less than center resolution. Is the decrease in resolution from center to corner linear? Are there any lenses that have the same corner and center resolution?

Optical Aberrations are radially dependent, with third order aberration terms including r^2, r^3, r^4. So, a center-focused, full-aperture, optical design will always have MTF degradation from center to corner.

However, you can 'flatten' the MTF vs. Field in three ways: 1.) Focus at an intermediary field angle between the center and edge, 2.) Stop down the lens to a higher F/#, 3.) Use an Optical Low-Pass Filter. Once the lens is diffraction limited, the resolution in the center will be the same as the corners. Both methods #2 and #3 may result in a lens-limited vision system.

I was hoping to get a 4/3" inch sensor format (Sony IMX540) which has pixel size 2.74 um and resolution 5320x4600. However all 8mm focal lenses I have seen so far (brand names kowa, navitar, fujinon) for 4/3" format are 160 lp/mm center and 80 lp/mm corner (I need 182 lp/mm). For the 1.1" sensor I have seen center/corner resolution of 200/100 lp/mm. It almost seems like getting the 4/3" sensor would give me similar image "quality" (sorry I don't know the appropriate word here) as the 1.1" sensor because of the low lens resolutions available for the 4/3" sensor. Am I correct in this interpretation?

This depends on the F/# of the lenses. Vendor MTF values are usually defined at full aperture (e.g. F/1.4), or near full aperture. Each vendor specifies these differently, so you'll need to check carefully. For a 2.74um pixel pitch, the Nyquist frequency is 91lp/mm, 129lp/mm, 182lp/mm for R/B, G, K correspondingly.

If you stop down the 160lp/mm 80lp/mm lens, you may be able to achieve the 129lp/mm across field, assuming an RGB variant of the camera. This would imply your system is sensor-limited, but require a longer exposure time. The Commonlands camera depth of field calculator provides the relative exposure length and shutter speed if you were to stop down the lens. Please check that an increased exposure length is compatible with the required framerate for your machine vision application.

If you have more questions, please reach out direct.