Adding poisson noise to a self made image

Hi,

I have seen similar questions

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to my own before, but unfortunately I have not managed to fix it. I want to use imnoise to apply a Poisson noise to an image. I suspect my problem is that I don't really understand the necessary scaling which in the documentation is supposed to be 1e12 or 1e6. As far as I understand this number is supposed to correspond to the number of photons per pixel. The Poisson distribution is , where as I understand λ is the expected number of photons per pixel, and k is the actual number of photons per pixel.

My code is the following:

imageSizeX = 500;

imageSizeY = 420;

image=zeros(imageSizeX,imageSizeY,3)+1; %initialize white background

image(150:350,190:240,1:3)=0; %Black object

imgGauss = imnoise(image,'gaussian'); %Adds Gaussian white noise

imgPoisson = imnoise(image/1e12,'poisson'); %Adds Poisson noise

figure(1)

imshow(image)

figure(2)

imshow(imgGauss)

figure(3)

imshow(imgPoisson)

The output of imshow(imgPoisson) is just a black image. Can anyone enlighten me, and hopefully others, how one is supposed to use the imnoise function with a very basic example as the one shown above?