def _synthZernikeRecFromWavefront(self, nModes, radiusInPixels):
diameterInPixels = 2 * radiusInPixels
zg = ZernikeGenerator(diameterInPixels)
wf = zg.getZernikeDict(list(range(2, 2 + nModes)))
im = np.zeros((nModes, wf[2].compressed().size))
modesIdx = list(range(2, 2 + nModes))
i = 0
for idx in modesIdx:
im[i, :] = wf[idx].compressed()
i += 1
return pinv2(im)
class TestZernikeGenerator(unittest.TestCase):
def setUp(self):
self._nPixels = 10
self.generator = ZernikeGenerator(self._nPixels)
def testPiston(self):
piston = self.generator[1]
self.assertEqual(piston.shape, (self._nPixels, self._nPixels))
self.assertTrue(piston.mask[0, 0])
self.assertAlmostEqual(piston[self._nPixels // 2, self._nPixels // 2],
1.)
def testTilt(self):
nPx = 128
generator = ZernikeGenerator(nPx)
tilt = generator[3]
self.assertAlmostEqual(tilt[-1, nPx // 2], 2. * (1 - 1. / nPx))
def testOdd(self):
nPx = 137
generator = ZernikeGenerator(nPx)
tilt = generator[17]
self.assertAlmostEqual(tilt[int(nPx / 2.), int(nPx / 2.)], 0.)
def testDegree(self):
m, n = ZernikeGenerator.degree(1)
self.assertEqual(m, 0)
self.assertEqual(n, 0)
m, n = ZernikeGenerator.degree(2)
self.assertEqual(m, 1)
self.assertEqual(n, 1)
m, n = ZernikeGenerator.degree(3)
self.assertEqual(m, 1)
self.assertEqual(n, 1)
m, n = ZernikeGenerator.degree(4)
self.assertEqual(m, 2)
self.assertEqual(n, 0)
m, n = self.generator.degree(2000000)
self.assertEqual(m, 1999)
self.assertEqual(n, 999)
def testRmn(self):
self.assertTrue(
np.allclose(self.generator._rnm(0, 0, np.array([0, 0.5, 1])),
np.array([1, 1, 1])))
self.assertTrue(
np.allclose(self.generator._rnm(1, 1, np.array([0, 0.5, 1])),
np.array([0, 0.5, 1])))
self.assertTrue(
np.allclose(self.generator._rnm(2, 0, np.array([0, 0.5, 1])),
np.array([-1, -0.5, 1])))
self.assertTrue(
np.allclose(self.generator._rnm(5, 1, np.array([0, 0.5, 1])),
np.array([0, 0.3125, 1])))
def testPolar(self):
self.assertTrue(
np.allclose(
self.generator._polar(1, np.array([0, 0.5, 1]),
np.array([0, 1, 5]) * np.pi / 4),
np.array([1, 1, 1])))
self.assertTrue(
np.allclose(
self.generator._polar(2, np.array([0, 0.5, 1]),
np.array([0, 1, 5]) * np.pi / 3),
np.array([0, 0.5, 1])))
self.assertTrue(
np.allclose(
self.generator._polar(3, np.array([0, 0.5, 1]),
np.array([0, 1, 5]) * np.pi / 3),
np.array([0, 0.866025, -1.73205])))
self.assertTrue(
np.allclose(
self.generator._polar(16, np.array([0, 0.5, 1]),
np.array([0, 1, 5]) * np.pi / 3),
np.array([0, 0.541266, 1.73205])))
def testDerivativeX(self):
gammaX = self.generator._derivativeCoeffX(30)
self.assertAlmostEqual(gammaX[1, 0], 2)
self.assertAlmostEqual(gammaX[15, 3], 6)
self.assertAlmostEqual(gammaX[16, 4], 3 * np.sqrt(2))
def testDerivativeX2(self):
gammaX = self.generator._derivativeCoeffX(2)
self.assertTrue(np.allclose(gammaX, np.array([[0., 0.], [2., 0.]])),
"%s" % str(gammaX))
def testDerivativeY3(self):
gammaY = self.generator._derivativeCoeffY(3)
self.assertTrue(
np.allclose(gammaY,
np.array([[0., 0., 0.], [0., 0., 0.], [2., 0., 0.]])),
"%s" % str(gammaY))
def testDerivativeY(self):
gammaY = self.generator._derivativeCoeffY(30)
self.assertAlmostEqual(gammaY[2, 0], 2)
self.assertAlmostEqual(gammaY[16, 3], 6)
self.assertAlmostEqual(gammaY[9, 4], -2 * np.sqrt(3))
def testRmsIsOne(self):
zg = ZernikeGenerator(512)
self.assertAlmostEqual(1., np.std(zg.getZernike(4)), 4)
def testGetItem(self):
a = self.generator[2]
b = self.generator.getZernike(2)
self.assertTrue(np.allclose(a, b))
def testGetZernikeDict(self):
dd = self.generator.getZernikeDict([1, 2, 10])
self.assertTrue(np.allclose([1, 2, 10], list(dd.keys())))
self.assertTrue(np.allclose(dd[10], self.generator.getZernike(10)))
def testGetDerivativeOfTip(self):
got = self.generator.getDerivativeX(2)
wanted = 2 * np.ones((self._nPixels, self._nPixels))
self.assertTrue(np.allclose(wanted, got),
"got %s, wanted %s" % (str(got), str(wanted)))
got = self.generator.getDerivativeY(2)
wanted = 0. * np.ones((self._nPixels, self._nPixels))
self.assertTrue(np.allclose(wanted, got),
"got %s, wanted %s" % (str(got), str(wanted)))
def testGetDerivativeOfTilt(self):
got = self.generator.getDerivativeX(3)
wanted = 0. * np.ones((self._nPixels, self._nPixels))
self.assertTrue(np.allclose(wanted, got),
"got %s, wanted %s" % (str(got), str(wanted)))
got = self.generator.getDerivativeY(3)
wanted = 2. * np.ones((self._nPixels, self._nPixels))
self.assertTrue(np.allclose(wanted, got),
"got %s, wanted %s" % (str(got), str(wanted)))