How to zoom into a specific latitude in cartopy.crs.Orthographic?

I'm unsure if this is possible, but I'm essentially trying to isolate the Arctic circle latitude (60N) in an orthographic map AND maintain the ellipsoid, not have the zoomed in image be a rectangle/square.

Here is what I have:

fig = plt.figure(figsize=[20, 10])

ax1 = plt.subplot(1, 1, 1, projection=ccrs.Orthographic(0, 90))

for ax in [ax1]:
    ax.coastlines(zorder=2)
    ax.stock_img()
    ax.gridlines()

This gives the north polar view I want, but I would like for it to stop at 60N.

To get a zoom-in and square extent of an orthographic map, You need to plot some control points (with .scatter, for example) or specify correct extent in projection coordinates (more difficult). Here is the code to try.

import cartopy
import cartopy.crs as ccrs
import matplotlib.pyplot as plt

fig = plt.figure(figsize=[8, 8])

lonlatproj = ccrs.PlateCarree()
my_projn = ccrs.Orthographic(central_longitude=0,central_latitude=90)

ax1 = plt.subplot(1, 1, 1, projection=my_projn)

# set `lowlat` as lower limits of latitude to plot some points
# these points will determine the plot extents of the map
lowlat = 60 + 2.8   # and get 60
lons, lats = [-180,-90,0,90], [lowlat,lowlat,lowlat,lowlat]
# plot invisible points to get map extents
ax1.scatter(lons, lats, s=0, color='r', transform=lonlatproj)
#ax1.stock_img()  #uncomment to get it plotted
ax1.coastlines(lw=0.5, zorder=2)
ax1.gridlines(lw=2, ec='black', draw_labels=True)

Method 2: By specifying correct extent in projection coordinates

import cartopy
import cartopy.crs as ccrs
import matplotlib.pyplot as plt

fig = plt.figure(figsize=[8, 8])

lonlatproj = ccrs.PlateCarree()
my_projn = ccrs.Orthographic(central_longitude=0,central_latitude=90)

ax1 = plt.subplot(1, 1, 1, projection=my_projn)

# These 2 lines of code grab extents in projection coordinates
_, y_min = my_projn.transform_point(0, 60, lonlatproj)  #(0.0, -3189068.5)
x_max, _ = my_projn.transform_point(90, 60, lonlatproj) #(3189068.5, 0)

# prep extents of the axis to plot map
pad = 25000
xmin,xmax,ymin,ymax = y_min-pad, x_max+pad, y_min-pad, x_max+pad
# set extents with prepped values
ax1.set_extent([xmin,xmax,ymin,ymax], crs=my_projn) # data/projection coordinates

ax1.stock_img()
ax1.coastlines(lw=0.5, zorder=2)

# plot other layers of data here using proper values of zorder

# finally, plot gridlines
ax1.gridlines(draw_labels=True, x_inline=False, y_inline=True,
              color='k', linestyle='dashed', linewidth=0.5)
plt.show()

Method 3 Plot the map with circular boundary

The runnable code:

import cartopy.crs as ccrs
import matplotlib.pyplot as plt
import matplotlib.path as mpath
import numpy as np

r_limit = 3214068.5 #from: ax.get_ylim() of above plot

# some settings  
lonlatproj = ccrs.PlateCarree()
my_projn = ccrs.Orthographic(central_longitude=0, central_latitude=90)
fig = plt.figure(figsize=[8, 8])
ax = plt.subplot(1, 1, 1, projection=my_projn)

# add bluemarble image
ax.stock_img()
# add coastlines
ax.coastlines(lw=0.5, color="black", zorder=20)


# draw graticule (of meridian and parallel lines)
gls = ax.gridlines(draw_labels=True, crs=ccrs.PlateCarree(), lw=3, color="gold",
        y_inline=True, xlocs=range(-180,180,30), ylocs=range(-80,91,10))


# add extra padding to the plot extents
r_extent = r_limit*1.0001
ax.set_xlim(-r_extent, r_extent)
ax.set_ylim(-r_extent, r_extent)


# Prep circular boundary
circle_path = mpath.Path.unit_circle()
circle_path = mpath.Path(circle_path.vertices.copy() * r_limit,
                           circle_path.codes.copy())

#set circle boundary
ax.set_boundary(circle_path)
#hide frame
ax.set_frame_on(False)  #hide the rectangle frame

plt.show()