In linear interpolation, there's too much white and not enough black. That's why gamma correction/sRGB exists after all: if you encode the linear value directly, you waste most of the space on white values you can barely tell apart.
sRGB: https://i.imgur.com/dbn3TM6.png Lab (linear): https://i.imgur.com/dCXzbF3.png
Please download the images and view in a proper image viewer. For some reason at least on my Windows machine Google Chrome adds horrible color banding to both images.
This is my code:
import imageio
import numpy as np
import colour
quantize_with_dither = lambda im: np.clip(im * (2**8-1) + np.random.uniform(size=im.shape), 0, 2**8-1).astype(np.uint8)
srgb_black = [0, 0, 0]
srgb_white = [1, 1, 1]
srgb_grad = np.linspace(srgb_black, srgb_white, 500) * np.ones((200, 1, 3))
imageio.imwrite("srgb.tif", quantize_with_dither(srgb_grad))
lab_black = colour.XYZ_to_Lab(colour.sRGB_to_XYZ(srgb_black))
lab_white = colour.XYZ_to_Lab(colour.sRGB_to_XYZ(srgb_white))
lab_grad = np.linspace(lab_black, lab_white, 500) * np.ones((200, 1, 3))
lab_grad_in_srgb = colour.XYZ_to_sRGB(colour.Lab_to_XYZ(lab_grad))
imageio.imwrite("lab.tif", quantize_with_dither(lab_grad_in_srgb))
magick convert lab.tif -set colorspace sRGB -depth 8 lab.png
magick convert srgb.tif -set colorspace sRGB -depth 8 srgb.pngGamma encoding is lin_to_srgb(c) = c*12.92 if c<=0.0031308 else 1.055*c**(1/2.4)-0.055. Since lin_to_srgb(0.214)=0.5, in a linear ramp, the middle gray (808080) pixel should occur about 20% of the way through.
https://i.imgur.com/jeM4RCu.png
top: linear_to_srgb(x)
middle: x
bottom: srgb_to_linear(x)