pkb = np.zeros((3,3))
pkb[1,1] = 1
pkb[0,1] = -1

dkb = np.zeros((3,3))
dkb[1,1] = 1
dkb[0,0] = -1/2

diffs = np.zeros(shape=(*a.shape, 8))
for rot in range(4):
    pk = np.rot90(pkb, k=rot)
    dk = np.rot90(dkb, k=rot)
    pc = correlate(a, pk, mode='constant', cval=0.0)
    dc = correlate(a, dk, mode='constant', cval=0.0)
    diffs[:, :, rot] = pc
    diffs[:, :, rot+4] = dc