diff --git a/src/ol/sphere.js b/src/ol/sphere.js
index 48af84e903..cbc9937b58 100644
--- a/src/ol/sphere.js
+++ b/src/ol/sphere.js
@@ -1,9 +1,9 @@
 /**
-* @license
-* Latitude/longitude spherical geodesy formulae taken from
-* http://www.movable-type.co.uk/scripts/latlong.html
-* Licensed under CC-BY-3.0.
-*/
+ * @license
+ * Latitude/longitude spherical geodesy formulae taken from
+ * http://www.movable-type.co.uk/scripts/latlong.html
+ * Licensed under CC-BY-3.0.
+ */
 
 /**
  * @module ol/sphere
@@ -13,12 +13,15 @@ import GeometryType from './geom/GeometryType.js';
 
 
 /**
- * Object literal with options for the {@link getLength} or
- * {@link getArea} functions.
- * @typedef {{projection: (ol.ProjectionLike|undefined),
- *    radius: (number|undefined)}}
+ * Object literal with options for the {@link getLength} or {@link getArea}
+ * functions.
+ * @typedef {Object} SphereMetricOptions
+ * @property {module:ol/types~ProjectionLike} [projection='EPSG:3857']
+ * Projection of the  geometry.  By default, the geometry is assumed to be in
+ * Web Mercator.
+ * @property {number} [radius=6371008.8] Sphere radius.  By default, the radius of the
+ * earth is used (Clarke 1866 Authalic Sphere).
  */
-export let SphereMetricOptions;
 
 
 /**
@@ -71,15 +74,10 @@ function getLengthInternal(coordinates, radius) {
  * great circle distances between coordinates.  For polygons, the length is
  * the sum of all rings.  For points, the length is zero.  For multi-part
  * geometries, the length is the sum of the length of each part.
- * @param {ol.geom.Geometry} geometry A geometry.
- * @param {SphereMetricOptions=} opt_options Options for the length
- *     calculation.  By default, geometries are assumed to be in 'EPSG:3857'.
- *     You can change this by providing a `projection` option.
- * @param {(ol.ProjectionLike|undefined)} opt_options.projection Projection of
- *     the geometry.  By default, the geometry is assumed to be in EPSG:3857
- *     (Web Mercator).
- * @param {(number|undefined)} opt_options.radius Sphere radius.  Defaults to
- *     the Earth's mean radius using the WGS84 ellipsoid.
+ * @param {module:ol/geom/Geometry~Geometry} geometry A geometry.
+ * @param {module:ol/sphere~SphereMetricOptions=} opt_options Options for the
+ * length calculation.  By default, geometries are assumed to be in 'EPSG:3857'.
+ * You can change this by providing a `projection` option.
  * @return {number} The spherical length (in meters).
  * @api
  */
@@ -100,20 +98,20 @@ export function getLength(geometry, opt_options) {
     }
     case GeometryType.LINE_STRING:
     case GeometryType.LINEAR_RING: {
-      coordinates = /** @type {ol.geom.SimpleGeometry} */ (geometry).getCoordinates();
+      coordinates = /** @type {module:ol/geom/SimpleGeometry~SimpleGeometry} */ (geometry).getCoordinates();
       length = getLengthInternal(coordinates, radius);
       break;
     }
     case GeometryType.MULTI_LINE_STRING:
     case GeometryType.POLYGON: {
-      coordinates = /** @type {ol.geom.SimpleGeometry} */ (geometry).getCoordinates();
+      coordinates = /** @type {module:ol/geom/SimpleGeometry~SimpleGeometry} */ (geometry).getCoordinates();
       for (i = 0, ii = coordinates.length; i < ii; ++i) {
         length += getLengthInternal(coordinates[i], radius);
       }
       break;
     }
     case GeometryType.MULTI_POLYGON: {
-      coordinates = /** @type {ol.geom.SimpleGeometry} */ (geometry).getCoordinates();
+      coordinates = /** @type {module:ol/geom/SimpleGeometry~SimpleGeometry} */ (geometry).getCoordinates();
       for (i = 0, ii = coordinates.length; i < ii; ++i) {
         coords = coordinates[i];
         for (j = 0, jj = coords.length; j < jj; ++j) {
@@ -123,7 +121,7 @@ export function getLength(geometry, opt_options) {
       break;
     }
     case GeometryType.GEOMETRY_COLLECTION: {
-      const geometries = /** @type {ol.geom.GeometryCollection} */ (geometry).getGeometries();
+      const geometries = /** @type {module:ol/geom/GeometryCollection~GeometryCollection} */ (geometry).getGeometries();
       for (i = 0, ii = geometries.length; i < ii; ++i) {
         length += getLength(geometries[i], opt_options);
       }
@@ -145,7 +143,7 @@ export function getLength(geometry, opt_options) {
  * Polygons on a Sphere", JPL Publication 07-03, Jet Propulsion
  * Laboratory, Pasadena, CA, June 2007
  *
- * @param {Array.<ol.Coordinate>} coordinates List of coordinates of a linear
+ * @param {Array.<module:ol/types~Coordinate>} coordinates List of coordinates of a linear
  * ring. If the ring is oriented clockwise, the area will be positive,
  * otherwise it will be negative.
  * @param {number} radius The sphere radius.
@@ -172,8 +170,8 @@ function getAreaInternal(coordinates, radius) {
 /**
  * Get the spherical area of a geometry.  This is the area (in meters) assuming
  * that polygon edges are segments of great circles on a sphere.
- * @param {ol.geom.Geometry} geometry A geometry.
- * @param {SphereMetricOptions=} opt_options Options for the area
+ * @param {module:ol/geom/Geometry~Geometry} geometry A geometry.
+ * @param {module:ol/sphere~SphereMetricOptions=} opt_options Options for the area
  *     calculation.  By default, geometries are assumed to be in 'EPSG:3857'.
  *     You can change this by providing a `projection` option.
  * @return {number} The spherical area (in square meters).
@@ -198,7 +196,7 @@ export function getArea(geometry, opt_options) {
       break;
     }
     case GeometryType.POLYGON: {
-      coordinates = /** @type {ol.geom.Polygon} */ (geometry).getCoordinates();
+      coordinates = /** @type {module:ol/geom/Polygon~Polygon} */ (geometry).getCoordinates();
       area = Math.abs(getAreaInternal(coordinates[0], radius));
       for (i = 1, ii = coordinates.length; i < ii; ++i) {
         area -= Math.abs(getAreaInternal(coordinates[i], radius));
@@ -206,7 +204,7 @@ export function getArea(geometry, opt_options) {
       break;
     }
     case GeometryType.MULTI_POLYGON: {
-      coordinates = /** @type {ol.geom.SimpleGeometry} */ (geometry).getCoordinates();
+      coordinates = /** @type {module:ol/geom/SimpleGeometry~SimpleGeometry} */ (geometry).getCoordinates();
       for (i = 0, ii = coordinates.length; i < ii; ++i) {
         coords = coordinates[i];
         area += Math.abs(getAreaInternal(coords[0], radius));
@@ -217,7 +215,7 @@ export function getArea(geometry, opt_options) {
       break;
     }
     case GeometryType.GEOMETRY_COLLECTION: {
-      const geometries = /** @type {ol.geom.GeometryCollection} */ (geometry).getGeometries();
+      const geometries = /** @type {module:ol/geom/GeometryCollection~GeometryCollection} */ (geometry).getGeometries();
       for (i = 0, ii = geometries.length; i < ii; ++i) {
         area += getArea(geometries[i], opt_options);
       }
@@ -234,13 +232,13 @@ export function getArea(geometry, opt_options) {
 /**
  * Returns the coordinate at the given distance and bearing from `c1`.
  *
- * @param {ol.Coordinate} c1 The origin point (`[lon, lat]` in degrees).
+ * @param {module:ol/types~Coordinate} c1 The origin point (`[lon, lat]` in degrees).
  * @param {number} distance The great-circle distance between the origin
  *     point and the target point.
  * @param {number} bearing The bearing (in radians).
  * @param {number=} opt_radius The sphere radius to use.  Defaults to the Earth's
  *     mean radius using the WGS84 ellipsoid.
- * @return {ol.Coordinate} The target point.
+ * @return {module:ol/types~Coordinate} The target point.
  */
 export function offset(c1, distance, bearing, opt_radius) {
   const radius = opt_radius || DEFAULT_RADIUS;