kymograph tutorial: add section on photon counts

docs/tutorial/kymographs.rst

@@ -142,40 +142,43 @@ This returns a new (but flipped) :class:`~lumicks.pylake.kymo.Kymo`::
 
 Extracting photon counts
 ------------------------
+
 Photon counts can be extracted from the raw image, for example for stoichiometry analysis.
 First, select a region for which the photon counts have to be determined::
 
-    kymo_selection = kymo["88.5s":"93s"].crop_by_distance(21.4,22.3)
+    kymo_selection = kymo["88.5s":"93s"].crop_by_distance(21.4, 22.3)
 
     plt.figure()
     kymo_selection.plot("rgb", adjustment=lk.ColorAdjustment(0, 98, mode="percentile"))
 
 Get the raw data (photon counts for each pixel) for the selected region::
 
-    selection_green = kymo_selection.get_image(channel = 'green')
+    selection_green = kymo_selection.get_image(channel="green")
 
 .. image:: figures/kymographs/kymograph_selection.png
 
 If the background has to be subtracted, choose a region without binding events as background::
 
-    background =  kymo["92.1s":"100s"].crop_by_distance(21.4,22.3)
+    background =  kymo["92.1s":"100s"].crop_by_distance(21.4, 22.3)
     
     plt.figure()
     background.plot("rgb", adjustment=lk.ColorAdjustment(0, 98, mode="percentile"))
 
 .. image:: figures/kymographs/background.png
 
-Subtract the background and sum over the vertical axis (along the width of the binding event) to obtain the photon counts over time::
+Sum over the vertical axis (along the width of the binding event) to obtain the total photon counts over the selected regions.
+Since every pixel has an average background signal of `background_mean`, we need to sum the background over the same region to obtain the total background.
 
-    background_mean = np.mean(background.get_image(channel = "green"))
-    photon_counts = np.sum(selection_green-background_mean, axis = 0)
-    time = np.arange(len(photon_counts))*kymo.line_time_seconds
+    summed_photon_counts = np.sum(selection_green, axis=0)
+    background_mean = np.mean(background.get_image(channel="green"))
+    summed_background = background_mean * selection_green.shape[0]
+    time = np.arange(len(photon_counts)) * kymo.line_time_seconds
 
     plt.figure()
-    plt.plot(time, photon_counts)
+    plt.plot(time, summed_photon_counts - summed_background)
     plt.xlabel("time (s)")
-    plt.ylabel("Photon counts")
-    plt.title("Photon counts along binding event")
+    plt.ylabel("Signal Intensity")
+    plt.title("Photon counts along binding event minus background")
 
 .. image:: figures/kymographs/photon_counts.png