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    "# Simulating Images\n",
    "\n",
    "In class, we talked about how a telescope's *optics* form an image at a focal plane and a telescope's *detector* records that image. We've added two cartoon functions to `henrietta` that help us understand the basics of this process: one that uses online star catalogs and your inputs to (very approximately) simulate a patch of the sky seen through the optics of a telescope, and one that simulates a detector recording that image."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt, numpy as np\n",
    "from henrietta import imaging"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Simulate the Optics of Our Telescope\n",
    "The `simulate_optics` function produces a simulation of the image that would appear at the focal plane of a telescope, expressed in units of photons/s/pixel. These images are \"perfect\", in the sense that they are an expectation for the rate at which photons will be hitting a detector."
   ]
  },
  {
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   "source": [
    "fluximage = imaging.simulate_optics(target='GJ 1132', \n",
    "                                    collectingarea=1.0, \n",
    "                                    pixelscale=21, \n",
    "                                    fov=180, \n",
    "                                    background=0.0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The `plt.imshow` function (with its many options!) can display that image for us to peruse."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "plt.imshow(fluximage)\n",
    "plt.colorbar(label='photons/s/pixel');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Simulate the Detector Behind Our Telescope\n",
    "The `simulate_detector` function takes an image at the focal plane (in photons/s), and simulates the total number of photons the detector would record. These are noisy images, with the effects of photon noise included."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "photonimage = imaging.simulate_detector(fluximage, \n",
    "                                        exptime=1.0, \n",
    "                                        quantumefficiency=0.001, \n",
    "                                        readnoise=10.0)\n",
    "plt.imshow(photonimage)\n",
    "plt.colorbar(label='photons/pixel');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If you run `simulate_detector` several times, you'll see you keep getting slightly different images. The function is simulating the actual detection of photons, and because we know photon-counting measurements always have uncertainties associated with them ($\\sigma = \\sqrt{N}$)ca"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Simulate Your Own Star, with your Own Telescope** \n",
    "\n",
    "Here are some ways you might think about playing with these tools: Pick a star and simulate some images. How does a flux image (photons/s/pixel) look different with Kepler, TESS, or a cell phone camera? How does the appearance of a photon image (photons/pixel) change if you change the exposure time? What challenges would be unique to each telescope? Play with the `background` keyword in `simulate_optics`; why is it difficult to see stars during the day (on Earth)?"
   ]
  }
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