From plt.imshow() official guide, we know that aspect controls the aspect ratio of the axes. Well in my words, the aspect is exactly the ratio of x unit and y unit. Most of the time we want to keep it as 1 since we do not want to distort out figures unintentionally. However, there is indeed cases that we need to specify aspect a value other than 1. The questioner provided a good example that x and y axis may have different physical units. Let's assume that x is in km and y in m. Hence for a 10x10 data, the extent should be [0,10km,0,10m] = [0, 10000m, 0, 10m]. In such case, if we continue to use the default aspect=1, the quality of the figure is really bad. We can hence specify aspect = 1000 to optimize our figure. The following codes illustrate this method.
%matplotlib inline
import numpy as np
import matplotlib.pyplot as plt
rng=np.random.RandomState(0)
data=rng.randn(10,10)
plt.imshow(data, origin = 'lower', extent = [0, 10000, 0, 10], aspect = 1000)
Nevertheless, I think there is an alternative that can meet the questioner's demand. We can just set the extent as [0,10,0,10] and add additional xy axis labels to denote the units. Codes as follows.
plt.imshow(data, origin = 'lower', extent = [0, 10, 0, 10])
plt.xlabel('km')
plt.ylabel('m')
To make a correct figure, we should always bear in mind that x_max-x_min = x_res * data.shape[1] and y_max - y_min = y_res * data.shape[0], where extent = [x_min, x_max, y_min, y_max]. By default, aspect = 1, meaning that the unit pixel is square. This default behavior also works fine for x_res and y_res that have different values. Extending the previous example, let's assume that x_res is 1.5 while y_res is 1. Hence extent should equal to [0,15,0,10]. Using the default aspect, we can have rectangular color pixels, whereas the unit pixel is still square!
plt.imshow(data, origin = 'lower', extent = [0, 15, 0, 10])
# Or we have similar x_max and y_max but different data.shape, leading to different color pixel res.
data=rng.randn(10,5)
plt.imshow(data, origin = 'lower', extent = [0, 5, 0, 5])
The aspect of color pixel is x_res / y_res. setting its aspect to the aspect of unit pixel (i.e. aspect = x_res / y_res = ((x_max - x_min) / data.shape[1]) / ((y_max - y_min) / data.shape[0])) would always give square color pixel. We can change aspect = 1.5 so that x-axis unit is 1.5 times y-axis unit, leading to a square color pixel and square whole figure but rectangular pixel unit. Apparently, it is not normally accepted.
data=rng.randn(10,10)
plt.imshow(data, origin = 'lower', extent = [0, 15, 0, 10], aspect = 1.5)
The most undesired case is that set aspect an arbitrary value, like 1.2, which will lead to neither square unit pixels nor square color pixels.
plt.imshow(data, origin = 'lower', extent = [0, 15, 0, 10], aspect = 1.2)
Long story short, it is always enough to set the correct extent and let the matplotlib do the remaining things for us (even though x_res!=y_res)! Change aspect only when it is a must.