diff --git a/photutils/aperture/attributes.py b/photutils/aperture/attributes.py
index 242a464de..ba1713d45 100644
--- a/photutils/aperture/attributes.py
+++ b/photutils/aperture/attributes.py
@@ -9,7 +9,7 @@
 import numpy as np
 
 __all__ = ['ApertureAttribute', 'PixelPositions', 'SkyCoordPositions',
-           'Scalar', 'PositiveScalar', 'AngleOrPixelScalarQuantity']
+           'Scalar', 'PositiveScalar', 'ScalarAngle', 'ScalarAngleOrPixel']
 
 
 class ApertureAttribute:
@@ -142,10 +142,13 @@ def _validate(self, value):
             raise TypeError(f'{self.name} must be a scalar angle')
 
 
-class AngleOrPixelScalarQuantity(ApertureAttribute):
+class ScalarAngleOrPixel(ApertureAttribute):
     """
-    Check that value is either an angular or a pixel scalar
-    `~astropy.units.Quantity`.
+    Check that value is a scalar angle, either as a
+    `~astropy.coordinates.Angle` or `~astropy.units.Quantity` with
+    angular units, or a scalar `~astropy.units.Quantity` in pixel units.
+
+    The value must be strictly positive (> 0).
     """
 
     def _validate(self, value):
@@ -157,6 +160,9 @@ def _validate(self, value):
                     value.unit == u.pixel):
                 raise ValueError(f'{self.name} must have angular or pixel '
                                  'units')
+
+            if not value > 0:
+                raise ValueError(f'{self.name} must be strictly positive')
         else:
-            raise TypeError(f'{self.name} must be an astropy Quantity '
-                            'instance')
+            raise TypeError(f'{self.name} must be a scalar angle or pixel '
+                            'Quantity')
diff --git a/photutils/aperture/circle.py b/photutils/aperture/circle.py
index 493f00385..d0da66a19 100644
--- a/photutils/aperture/circle.py
+++ b/photutils/aperture/circle.py
@@ -8,8 +8,8 @@
 
 import numpy as np
 
-from .attributes import (AngleOrPixelScalarQuantity, PixelPositions,
-                         PositiveScalar, SkyCoordPositions)
+from .attributes import (PixelPositions, PositiveScalar, SkyCoordPositions,
+                         ScalarAngleOrPixel)
 from .core import PixelAperture, SkyAperture
 from .mask import ApertureMask
 from ..geometry import circular_overlap_grid
@@ -370,7 +370,7 @@ class SkyCircularAperture(SkyAperture):
     positions = SkyCoordPositions(
         'positions',
         description='The center position(s) in sky coordinates.')
-    r = AngleOrPixelScalarQuantity(
+    r = ScalarAngleOrPixel(
         'r',
         description='The radius, in angular or pixel units.')
 
@@ -433,10 +433,10 @@ class SkyCircularAnnulus(SkyAperture):
     positions = SkyCoordPositions(
         'positions',
         description='The center position(s) in sky coordinates.')
-    r_in = AngleOrPixelScalarQuantity(
+    r_in = ScalarAngleOrPixel(
         'r_in',
         description='The inner radius, in angular or pixel units.')
-    r_out = AngleOrPixelScalarQuantity(
+    r_out = ScalarAngleOrPixel(
         'r_out',
         description='The outer radius, in angular or pixel units.')
 
diff --git a/photutils/aperture/ellipse.py b/photutils/aperture/ellipse.py
index f4b7ffe09..4dc30d6ca 100644
--- a/photutils/aperture/ellipse.py
+++ b/photutils/aperture/ellipse.py
@@ -9,8 +9,8 @@
 import astropy.units as u
 import numpy as np
 
-from .attributes import (AngleOrPixelScalarQuantity, ScalarAngle, PixelPositions,
-                         PositiveScalar, Scalar, SkyCoordPositions)
+from .attributes import (ScalarAngle, PixelPositions, PositiveScalar, Scalar,
+                         SkyCoordPositions, ScalarAngleOrPixel)
 from .core import PixelAperture, SkyAperture
 from .mask import ApertureMask
 from ..geometry import elliptical_overlap_grid
@@ -455,10 +455,10 @@ class SkyEllipticalAperture(SkyAperture):
     positions = SkyCoordPositions(
         'positions',
         description='The center position(s) in sky coordinates.')
-    a = AngleOrPixelScalarQuantity(
+    a = ScalarAngleOrPixel(
         'a',
         description='The semimajor axis, in angular or pixel units.')
-    b = AngleOrPixelScalarQuantity(
+    b = ScalarAngleOrPixel(
         'b',
         description='The semiminor axis, in angular or pixel units.')
     theta = ScalarAngle(
@@ -546,16 +546,16 @@ class SkyEllipticalAnnulus(SkyAperture):
     positions = SkyCoordPositions(
         'positions',
         description='The center position(s) in sky coordinates.')
-    a_in = AngleOrPixelScalarQuantity(
+    a_in = ScalarAngleOrPixel(
         'a_in',
         description='The inner semimajor axis, in angular or pixel units.')
-    a_out = AngleOrPixelScalarQuantity(
+    a_out = ScalarAngleOrPixel(
         'a_out',
         description='The outer semimajor axis, in angular or pixel units.')
-    b_in = AngleOrPixelScalarQuantity(
+    b_in = ScalarAngleOrPixel(
         'b_in',
         description='The inner semiminor axis, in angular or pixel units.')
-    b_out = AngleOrPixelScalarQuantity(
+    b_out = ScalarAngleOrPixel(
         'b_out',
         description='The outer semiminor axis, in angular or pixel units.')
     theta = ScalarAngle(
diff --git a/photutils/aperture/rectangle.py b/photutils/aperture/rectangle.py
index 398db667e..3ee7912f3 100644
--- a/photutils/aperture/rectangle.py
+++ b/photutils/aperture/rectangle.py
@@ -9,8 +9,8 @@
 import astropy.units as u
 import numpy as np
 
-from .attributes import (AngleOrPixelScalarQuantity, ScalarAngle, PixelPositions,
-                         PositiveScalar, Scalar, SkyCoordPositions)
+from .attributes import (ScalarAngle, PixelPositions, PositiveScalar, Scalar,
+                         SkyCoordPositions, ScalarAngleOrPixel)
 from .core import PixelAperture, SkyAperture
 from .mask import ApertureMask
 from ..geometry import rectangular_overlap_grid
@@ -493,10 +493,10 @@ class SkyRectangularAperture(SkyAperture):
     positions = SkyCoordPositions(
         'positions',
         description='The center position(s) in sky coordinates.')
-    w = AngleOrPixelScalarQuantity(
+    w = ScalarAngleOrPixel(
         'w',
         description='The full width, in angular or pixel units.')
-    h = AngleOrPixelScalarQuantity(
+    h = ScalarAngleOrPixel(
         'h',
         description='The full height, in angular or pixel units.')
     theta = ScalarAngle(
@@ -592,16 +592,16 @@ class SkyRectangularAnnulus(SkyAperture):
     positions = SkyCoordPositions(
         'positions',
         description='The center position(s) in sky coordinates.')
-    w_in = AngleOrPixelScalarQuantity(
+    w_in = ScalarAngleOrPixel(
         'w_in',
         description='The inner full width, in angular or pixel units.')
-    w_out = AngleOrPixelScalarQuantity(
+    w_out = ScalarAngleOrPixel(
         'w_out',
         description='The outer full width, in angular or pixel units.')
-    h_in = AngleOrPixelScalarQuantity(
+    h_in = ScalarAngleOrPixel(
         'h_in',
         description='The inner full height, in angular or pixel units.')
-    h_out = AngleOrPixelScalarQuantity(
+    h_out = ScalarAngleOrPixel(
         'h_out',
         description='The outer full height, in angular or pixel units.')
     theta = ScalarAngle(