diff --git a/include/openmc/tallies/filter.h b/include/openmc/tallies/filter.h
index 9398d3ab87..286497d37a 100644
--- a/include/openmc/tallies/filter.h
+++ b/include/openmc/tallies/filter.h
@@ -7,7 +7,7 @@
 
 #include "openmc/hdf5_interface.h"
 #include "openmc/particle.h"
-#include "openmc/xml_interface.h"
+#include "pugixml.hpp"
 
 
 namespace openmc {
@@ -43,10 +43,10 @@ public:
 class Filter
 {
 public:
-  virtual std::string type() const = 0;
-
   virtual ~Filter() = 0;
 
+  virtual std::string type() const = 0;
+
   //! Uses an XML input to fill the filter's data fields.
   virtual void from_xml(pugi::xml_node node) = 0;
 
@@ -55,7 +55,7 @@ public:
   //! \param[out] match will contain the matching bins and corresponding
   //!   weights; note that there may be zero matching bins
   virtual void
-  get_all_bins(Particle* p, int estimator, FilterMatch& match) const = 0;
+  get_all_bins(const Particle* p, int estimator, FilterMatch& match) const = 0;
 
   //! Writes data describing this filter to an HDF5 statepoint group.
   virtual void
diff --git a/include/openmc/tallies/filter_azimuthal.h b/include/openmc/tallies/filter_azimuthal.h
index fdbe20ca55..b896400315 100644
--- a/include/openmc/tallies/filter_azimuthal.h
+++ b/include/openmc/tallies/filter_azimuthal.h
@@ -21,7 +21,7 @@ public:
 
   void from_xml(pugi::xml_node node) override;
 
-  void get_all_bins(Particle* p, int estimator, FilterMatch& match)
+  void get_all_bins(const Particle* p, int estimator, FilterMatch& match)
   const override;
 
   void to_statepoint(hid_t filter_group) const override;
diff --git a/include/openmc/tallies/filter_cell.h b/include/openmc/tallies/filter_cell.h
index 38cb1e57e5..9c654e82ed 100644
--- a/include/openmc/tallies/filter_cell.h
+++ b/include/openmc/tallies/filter_cell.h
@@ -24,14 +24,17 @@ public:
 
   void initialize() override;
 
-  void get_all_bins(Particle* p, int estimator, FilterMatch& match)
+  void get_all_bins(const Particle* p, int estimator, FilterMatch& match)
   const override;
 
   void to_statepoint(hid_t filter_group) const override;
 
   std::string text_label(int bin) const override;
 
+  //! The indices of the cells binned by this filter.
   std::vector<int32_t> cells_;
+
+  //! A map from cell indices to filter bin indices.
   std::unordered_map<int32_t, int> map_;
 };
 
diff --git a/include/openmc/tallies/filter_cellborn.h b/include/openmc/tallies/filter_cellborn.h
index 414a96ec72..400e82c282 100644
--- a/include/openmc/tallies/filter_cellborn.h
+++ b/include/openmc/tallies/filter_cellborn.h
@@ -16,7 +16,7 @@ class CellbornFilter : public CellFilter
 public:
   std::string type() const override {return "cellborn";}
 
-  void get_all_bins(Particle* p, int estimator, FilterMatch& match)
+  void get_all_bins(const Particle* p, int estimator, FilterMatch& match)
   const override;
 
   std::string text_label(int bin) const override;
diff --git a/include/openmc/tallies/filter_cellfrom.h b/include/openmc/tallies/filter_cellfrom.h
index 0826c669bf..bd3e08dcbb 100644
--- a/include/openmc/tallies/filter_cellfrom.h
+++ b/include/openmc/tallies/filter_cellfrom.h
@@ -16,7 +16,7 @@ class CellFromFilter : public CellFilter
 public:
   std::string type() const override {return "cellfrom";}
 
-  void get_all_bins(Particle* p, int estimator, FilterMatch& match)
+  void get_all_bins(const Particle* p, int estimator, FilterMatch& match)
   const override;
 
   std::string text_label(int bin) const override;
diff --git a/include/openmc/tallies/filter_distribcell.h b/include/openmc/tallies/filter_distribcell.h
index e66ee62130..73857e7cb0 100644
--- a/include/openmc/tallies/filter_distribcell.h
+++ b/include/openmc/tallies/filter_distribcell.h
@@ -22,7 +22,7 @@ public:
 
   void initialize() override;
 
-  void get_all_bins(Particle* p, int estimator, FilterMatch& match)
+  void get_all_bins(const Particle* p, int estimator, FilterMatch& match)
   const override;
 
   void to_statepoint(hid_t filter_group) const override;
diff --git a/include/openmc/tallies/filter_energyfunc.h b/include/openmc/tallies/filter_energyfunc.h
index 8fb1b9edee..6f51826267 100644
--- a/include/openmc/tallies/filter_energyfunc.h
+++ b/include/openmc/tallies/filter_energyfunc.h
@@ -27,14 +27,17 @@ public:
 
   void from_xml(pugi::xml_node node) override;
 
-  void get_all_bins(Particle* p, int estimator, FilterMatch& match)
+  void get_all_bins(const Particle* p, int estimator, FilterMatch& match)
   const override;
 
   void to_statepoint(hid_t filter_group) const override;
 
   std::string text_label(int bin) const override;
 
+  //! Incident neutron energy interpolation grid.
   std::vector<double> energy_;
+
+  //! Interpolant values.
   std::vector<double> y_;
 };
 
diff --git a/include/openmc/tallies/filter_legendre.h b/include/openmc/tallies/filter_legendre.h
index fabb8140b0..054ba14e79 100644
--- a/include/openmc/tallies/filter_legendre.h
+++ b/include/openmc/tallies/filter_legendre.h
@@ -20,7 +20,7 @@ public:
 
   void from_xml(pugi::xml_node node) override;
 
-  void get_all_bins(Particle* p, int estimator, FilterMatch& match)
+  void get_all_bins(const Particle* p, int estimator, FilterMatch& match)
   const override;
 
   void to_statepoint(hid_t filter_group) const override;
diff --git a/include/openmc/tallies/filter_material.h b/include/openmc/tallies/filter_material.h
index e78b056a43..d272451db5 100644
--- a/include/openmc/tallies/filter_material.h
+++ b/include/openmc/tallies/filter_material.h
@@ -24,14 +24,17 @@ public:
 
   void initialize() override;
 
-  void get_all_bins(Particle* p, int estimator, FilterMatch& match)
+  void get_all_bins(const Particle* p, int estimator, FilterMatch& match)
   const override;
 
   void to_statepoint(hid_t filter_group) const override;
 
   std::string text_label(int bin) const override;
 
+  //! The indices of the materials binned by this filter.
   std::vector<int32_t> materials_;
+
+  //! A map from material indices to filter bin indices.
   std::unordered_map<int32_t, int> map_;
 };
 
diff --git a/include/openmc/tallies/filter_mesh.h b/include/openmc/tallies/filter_mesh.h
index 98853e653e..250eb00e0a 100644
--- a/include/openmc/tallies/filter_mesh.h
+++ b/include/openmc/tallies/filter_mesh.h
@@ -22,7 +22,7 @@ public:
 
   void from_xml(pugi::xml_node node) override;
 
-  void get_all_bins(Particle* p, int estimator, FilterMatch& match)
+  void get_all_bins(const Particle* p, int estimator, FilterMatch& match)
   const override;
 
   void to_statepoint(hid_t filter_group) const override;
diff --git a/include/openmc/tallies/filter_meshsurface.h b/include/openmc/tallies/filter_meshsurface.h
index 2d5aefef67..08218ac3d4 100644
--- a/include/openmc/tallies/filter_meshsurface.h
+++ b/include/openmc/tallies/filter_meshsurface.h
@@ -12,7 +12,7 @@ public:
 
   void from_xml(pugi::xml_node node) override;
 
-  void get_all_bins(Particle* p, int estimator, FilterMatch& match)
+  void get_all_bins(const Particle* p, int estimator, FilterMatch& match)
   const override;
 
   std::string text_label(int bin) const override;
diff --git a/include/openmc/tallies/filter_mu.h b/include/openmc/tallies/filter_mu.h
index fdc311b276..68b2f7b023 100644
--- a/include/openmc/tallies/filter_mu.h
+++ b/include/openmc/tallies/filter_mu.h
@@ -21,7 +21,7 @@ public:
 
   void from_xml(pugi::xml_node node) override;
 
-  void get_all_bins(Particle* p, int estimator, FilterMatch& match)
+  void get_all_bins(const Particle* p, int estimator, FilterMatch& match)
   const override;
 
   void to_statepoint(hid_t filter_group) const override;
diff --git a/include/openmc/tallies/filter_polar.h b/include/openmc/tallies/filter_polar.h
index 3cc113a4fc..2bcdcd07f4 100644
--- a/include/openmc/tallies/filter_polar.h
+++ b/include/openmc/tallies/filter_polar.h
@@ -21,7 +21,7 @@ public:
 
   void from_xml(pugi::xml_node node) override;
 
-  void get_all_bins(Particle* p, int estimator, FilterMatch& match)
+  void get_all_bins(const Particle* p, int estimator, FilterMatch& match)
   const override;
 
   void to_statepoint(hid_t filter_group) const override;
diff --git a/include/openmc/tallies/filter_sph_harm.h b/include/openmc/tallies/filter_sph_harm.h
index 8e429b9538..786ef1a587 100644
--- a/include/openmc/tallies/filter_sph_harm.h
+++ b/include/openmc/tallies/filter_sph_harm.h
@@ -25,7 +25,7 @@ public:
 
   void from_xml(pugi::xml_node node) override;
 
-  void get_all_bins(Particle* p, int estimator, FilterMatch& match)
+  void get_all_bins(const Particle* p, int estimator, FilterMatch& match)
   const override;
 
   void to_statepoint(hid_t filter_group) const override;
@@ -33,6 +33,8 @@ public:
   std::string text_label(int bin) const override;
 
   int order_;
+
+  //! The type of angle that this filter measures when binning events.
   SphericalHarmonicsCosine cosine_ {SphericalHarmonicsCosine::particle};
 };
 
diff --git a/include/openmc/tallies/filter_sptl_legendre.h b/include/openmc/tallies/filter_sptl_legendre.h
index 5602395699..1b94ecf3db 100644
--- a/include/openmc/tallies/filter_sptl_legendre.h
+++ b/include/openmc/tallies/filter_sptl_legendre.h
@@ -25,7 +25,7 @@ public:
 
   void from_xml(pugi::xml_node node) override;
 
-  void get_all_bins(Particle* p, int estimator, FilterMatch& match)
+  void get_all_bins(const Particle* p, int estimator, FilterMatch& match)
   const override;
 
   void to_statepoint(hid_t filter_group) const override;
@@ -33,8 +33,15 @@ public:
   std::string text_label(int bin) const override;
 
   int order_;
+
+  //! The Cartesian coordinate axis that the Legendre expansion is applied to.
   LegendreAxis axis_;
-  double min_, max_;
+
+  //! The minimum coordinate along the reference axis that the expansion covers.
+  double min_;
+
+  //! The maximum coordinate along the reference axis that the expansion covers.
+  double max_;
 };
 
 } // namespace openmc
diff --git a/include/openmc/tallies/filter_surface.h b/include/openmc/tallies/filter_surface.h
index 85af6d0048..ea4dc5b990 100644
--- a/include/openmc/tallies/filter_surface.h
+++ b/include/openmc/tallies/filter_surface.h
@@ -24,14 +24,17 @@ public:
 
   void initialize() override;
 
-  void get_all_bins(Particle* p, int estimator, FilterMatch& match)
+  void get_all_bins(const Particle* p, int estimator, FilterMatch& match)
   const override;
 
   void to_statepoint(hid_t filter_group) const override;
 
   std::string text_label(int bin) const override;
 
+  //! The indices of the surfaces binned by this filter.
   std::vector<int32_t> surfaces_;
+
+  //! A map from surface indices to filter bin indices.
   std::unordered_map<int32_t, int> map_;
 };
 
diff --git a/include/openmc/tallies/filter_universe.h b/include/openmc/tallies/filter_universe.h
index 5e7c85d1f8..3ae0093cbd 100644
--- a/include/openmc/tallies/filter_universe.h
+++ b/include/openmc/tallies/filter_universe.h
@@ -24,14 +24,17 @@ public:
 
   void initialize() override;
 
-  void get_all_bins(Particle* p, int estimator, FilterMatch& match)
+  void get_all_bins(const Particle* p, int estimator, FilterMatch& match)
   const override;
 
   void to_statepoint(hid_t filter_group) const override;
 
   std::string text_label(int bin) const override;
 
+  //! The indices of the universes binned by this filter.
   std::vector<int32_t> universes_;
+
+  //! A map from universe indices to filter bin indices.
   std::unordered_map<int32_t, int> map_;
 };
 
diff --git a/include/openmc/tallies/filter_zernike.h b/include/openmc/tallies/filter_zernike.h
index 6450c6c172..19fff13363 100644
--- a/include/openmc/tallies/filter_zernike.h
+++ b/include/openmc/tallies/filter_zernike.h
@@ -20,17 +20,28 @@ public:
 
   void from_xml(pugi::xml_node node) override;
 
-  void get_all_bins(Particle* p, int estimator, FilterMatch& match)
+  void get_all_bins(const Particle* p, int estimator, FilterMatch& match)
   const override;
 
   void to_statepoint(hid_t filter_group) const override;
 
   std::string text_label(int bin) const override;
 
-  virtual void calc_n_bins() {n_bins_ = ((order_+1) * (order_+2)) / 2;}
+  int order() const {return order_;}
 
+  virtual void set_order(int order);
+
+  //! Cartesian x coordinate for the origin of this expansion.
+  double x_;
+
+  //! Cartesian y coordinate for the origin of this expansion.
+  double y_;
+
+  //! Maximum radius from the origin covered by this expansion.
+  double r_;
+
+protected:
   int order_;
-  double x_, y_, r_;
 };
 
 //==============================================================================
@@ -42,12 +53,12 @@ class ZernikeRadialFilter : public ZernikeFilter
 public:
   std::string type() const override {return "zernikeradial";}
 
-  void get_all_bins(Particle* p, int estimator, FilterMatch& match)
+  void get_all_bins(const Particle* p, int estimator, FilterMatch& match)
   const override;
 
   std::string text_label(int bin) const override;
 
-  void calc_n_bins() override {n_bins_ = order_ / 2 + 1;}
+  void set_order(int order) override;
 };
 
 } // namespace openmc
diff --git a/src/tallies/filter_azimuthal.cpp b/src/tallies/filter_azimuthal.cpp
index 7611cb1f18..99a649cd91 100644
--- a/src/tallies/filter_azimuthal.cpp
+++ b/src/tallies/filter_azimuthal.cpp
@@ -6,6 +6,7 @@
 #include "openmc/constants.h"
 #include "openmc/error.h"
 #include "openmc/search.h"
+#include "openmc/xml_interface.h"
 
 namespace openmc {
 
@@ -36,8 +37,8 @@ AzimuthalFilter::from_xml(pugi::xml_node node)
 }
 
 void
-AzimuthalFilter::get_all_bins(Particle* p, int estimator, FilterMatch& match)
-const
+AzimuthalFilter::get_all_bins(const Particle* p, int estimator,
+                              FilterMatch& match) const
 {
   double phi;
   if (estimator == ESTIMATOR_TRACKLENGTH) {
@@ -46,10 +47,11 @@ const
     phi = std::atan2(p->last_uvw[1], p->last_uvw[0]);
   }
 
-  if (phi >= bins_[0] && phi <= bins_.back()) {
+  if (phi >= bins_.front() && phi <= bins_.back()) {
+    //TODO: off-by-one
     auto bin = lower_bound_index(bins_.begin(), bins_.end(), phi) + 1;
     match.bins_.push_back(bin);
-    match.weights_.push_back(1);
+    match.weights_.push_back(1.0);
   }
 }
 
diff --git a/src/tallies/filter_cell.cpp b/src/tallies/filter_cell.cpp
index d52c6bb5f4..a09c331bf9 100644
--- a/src/tallies/filter_cell.cpp
+++ b/src/tallies/filter_cell.cpp
@@ -5,6 +5,7 @@
 #include "openmc/capi.h"
 #include "openmc/cell.h"
 #include "openmc/error.h"
+#include "openmc/xml_interface.h"
 
 namespace openmc {
 
@@ -18,6 +19,7 @@ CellFilter::from_xml(pugi::xml_node node)
 void
 CellFilter::initialize()
 {
+  // Convert cell IDs to indices of the global array.
   for (auto& c : cells_) {
     auto search = cell_map.find(c);
     if (search != cell_map.end()) {
@@ -29,19 +31,22 @@ CellFilter::initialize()
     }
   }
 
+  // Populate the index->bin map.
   for (int i = 0; i < cells_.size(); i++) {
     map_[cells_[i]] = i;
   }
 }
 
 void
-CellFilter::get_all_bins(Particle* p, int estimator, FilterMatch& match) const
+CellFilter::get_all_bins(const Particle* p, int estimator,
+                         FilterMatch& match) const
 {
   for (int i = 0; i < p->n_coord; i++) {
     auto search = map_.find(p->coord[i].cell);
     if (search != map_.end()) {
+      //TODO: off-by-one
       match.bins_.push_back(search->second + 1);
-      match.weights_.push_back(1);
+      match.weights_.push_back(1.0);
     }
   }
 }
diff --git a/src/tallies/filter_cellborn.cpp b/src/tallies/filter_cellborn.cpp
index c427401198..e77c2e42f7 100644
--- a/src/tallies/filter_cellborn.cpp
+++ b/src/tallies/filter_cellborn.cpp
@@ -5,13 +5,14 @@
 namespace openmc {
 
 void
-CellbornFilter::get_all_bins(Particle* p, int estimator, FilterMatch& match)
-const
+CellbornFilter::get_all_bins(const Particle* p, int estimator,
+                             FilterMatch& match) const
 {
   auto search = map_.find(p->cell_born);
   if (search != map_.end()) {
+    //TODO: off-by-one
     match.bins_.push_back(search->second + 1);
-    match.weights_.push_back(1);
+    match.weights_.push_back(1.0);
   }
 }
 
diff --git a/src/tallies/filter_cellfrom.cpp b/src/tallies/filter_cellfrom.cpp
index 5771f0b137..4ce24e8900 100644
--- a/src/tallies/filter_cellfrom.cpp
+++ b/src/tallies/filter_cellfrom.cpp
@@ -5,14 +5,15 @@
 namespace openmc {
 
 void
-CellFromFilter::get_all_bins(Particle* p, int estimator, FilterMatch& match)
-const
+CellFromFilter::get_all_bins(const Particle* p, int estimator,
+                             FilterMatch& match) const
 {
   for (int i = 0; i < p->last_n_coord; i++) {
     auto search = map_.find(p->last_cell[i]);
     if (search != map_.end()) {
+      //TODO: off-by-one
       match.bins_.push_back(search->second + 1);
-      match.weights_.push_back(1);
+      match.weights_.push_back(1.0);
     }
   }
 }
diff --git a/src/tallies/filter_distribcell.cpp b/src/tallies/filter_distribcell.cpp
index db1cd59c9f..f1e69b62a0 100644
--- a/src/tallies/filter_distribcell.cpp
+++ b/src/tallies/filter_distribcell.cpp
@@ -4,6 +4,7 @@
 #include "openmc/error.h"
 #include "openmc/geometry_aux.h" // For distribcell_path
 #include "openmc/lattice.h"
+#include "openmc/xml_interface.h"
 
 namespace openmc {
 
@@ -20,6 +21,7 @@ DistribcellFilter::from_xml(pugi::xml_node node)
 void
 DistribcellFilter::initialize()
 {
+  // Convert the cell ID to an index of the global array.
   auto search = cell_map.find(cell_);
   if (search != cell_map.end()) {
     cell_ = search->second;
@@ -33,8 +35,8 @@ DistribcellFilter::initialize()
 }
 
 void
-DistribcellFilter::get_all_bins(Particle* p, int estimator, FilterMatch& match)
-const
+DistribcellFilter::get_all_bins(const Particle* p, int estimator,
+                                FilterMatch& match) const
 {
   int offset = 0;
   auto distribcell_index = cells[cell_]->distribcell_index_;
@@ -52,8 +54,9 @@ const
       }
     }
     if (cell_ == p->coord[i].cell) {
+      //TODO: off-by-one
       match.bins_.push_back(offset + 1);
-      match.weights_.push_back(1);
+      match.weights_.push_back(1.0);
       return;
     }
   }
diff --git a/src/tallies/filter_energyfunc.cpp b/src/tallies/filter_energyfunc.cpp
index 92c9592a0b..b47e7b7b63 100644
--- a/src/tallies/filter_energyfunc.cpp
+++ b/src/tallies/filter_energyfunc.cpp
@@ -7,6 +7,7 @@
 #include "openmc/error.h"
 #include "openmc/search.h"
 #include "openmc/settings.h"
+#include "openmc/xml_interface.h"
 
 namespace openmc {
 
@@ -29,7 +30,7 @@ EnergyFunctionFilter::from_xml(pugi::xml_node node)
 }
 
 void
-EnergyFunctionFilter::get_all_bins(Particle* p, int estimator,
+EnergyFunctionFilter::get_all_bins(const Particle* p, int estimator,
                                    FilterMatch& match) const
 {
   if (p->last_E >= energy_.front() && p->last_E <= energy_.back()) {
@@ -40,6 +41,7 @@ EnergyFunctionFilter::get_all_bins(Particle* p, int estimator,
     double f = (p->last_E - energy_[i]) / (energy_[i+1] - energy_[i]);
 
     // Interpolate on the lin-lin grid.
+    //TODO: off-by-one
     match.bins_.push_back(1);
     match.weights_.push_back((1-f) * y_[i] + f * y_[i+1]);
   }
diff --git a/src/tallies/filter_legendre.cpp b/src/tallies/filter_legendre.cpp
index c8666f6b9b..32cedcfa0b 100644
--- a/src/tallies/filter_legendre.cpp
+++ b/src/tallies/filter_legendre.cpp
@@ -3,6 +3,7 @@
 #include "openmc/capi.h"
 #include "openmc/error.h"
 #include "openmc/math_functions.h"
+#include "openmc/xml_interface.h"
 
 namespace openmc {
 
@@ -14,12 +15,13 @@ LegendreFilter::from_xml(pugi::xml_node node)
 }
 
 void
-LegendreFilter::get_all_bins(Particle* p, int estimator, FilterMatch& match)
-const
+LegendreFilter::get_all_bins(const Particle* p, int estimator,
+                             FilterMatch& match) const
 {
   double wgt[n_bins_];
   calc_pn_c(order_, p->mu, wgt);
   for (int i = 0; i < n_bins_; i++) {
+    //TODO: off-by-one
     match.bins_.push_back(i + 1);
     match.weights_.push_back(wgt[i]);
   }
diff --git a/src/tallies/filter_material.cpp b/src/tallies/filter_material.cpp
index 66d9480883..2b6542d789 100644
--- a/src/tallies/filter_material.cpp
+++ b/src/tallies/filter_material.cpp
@@ -5,6 +5,7 @@
 #include "openmc/capi.h"
 #include "openmc/error.h"
 #include "openmc/material.h"
+#include "openmc/xml_interface.h"
 
 namespace openmc {
 
@@ -18,6 +19,7 @@ MaterialFilter::from_xml(pugi::xml_node node)
 void
 MaterialFilter::initialize()
 {
+  // Convert material IDs to indices of the global array.
   for (auto& m : materials_) {
     auto search = material_map.find(m);
     if (search != material_map.end()) {
@@ -30,19 +32,21 @@ MaterialFilter::initialize()
     }
   }
 
+  // Populate the index->bin map.
   for (int i = 0; i < materials_.size(); i++) {
     map_[materials_[i]] = i;
   }
 }
 
 void
-MaterialFilter::get_all_bins(Particle* p, int estimator, FilterMatch& match)
-const
+MaterialFilter::get_all_bins(const Particle* p, int estimator,
+                             FilterMatch& match) const
 {
   auto search = map_.find(p->material - 1);
   if (search != map_.end()) {
+    //TODO: off-by-one
     match.bins_.push_back(search->second + 1);
-    match.weights_.push_back(1);
+    match.weights_.push_back(1.0);
   }
 }
 
diff --git a/src/tallies/filter_mesh.cpp b/src/tallies/filter_mesh.cpp
index ad17543c6b..41b8e642bf 100644
--- a/src/tallies/filter_mesh.cpp
+++ b/src/tallies/filter_mesh.cpp
@@ -6,6 +6,7 @@
 #include "openmc/constants.h"
 #include "openmc/error.h"
 #include "openmc/mesh.h"
+#include "openmc/xml_interface.h"
 
 namespace openmc {
 
@@ -33,12 +34,13 @@ MeshFilter::from_xml(pugi::xml_node node)
 }
 
 void
-MeshFilter::get_all_bins(Particle* p, int estimator, FilterMatch& match)
+MeshFilter::get_all_bins(const Particle* p, int estimator, FilterMatch& match)
 const
 {
   if (estimator != ESTIMATOR_TRACKLENGTH) {
     auto bin = meshes[mesh_]->get_bin(p->coord[0].xyz);
     if (bin >= 0) {
+      //TODO: off-by-one
       match.bins_.push_back(bin);
       match.weights_.push_back(1.0);
     }
diff --git a/src/tallies/filter_meshsurface.cpp b/src/tallies/filter_meshsurface.cpp
index 124d3df33f..aafa91e6e2 100644
--- a/src/tallies/filter_meshsurface.cpp
+++ b/src/tallies/filter_meshsurface.cpp
@@ -16,8 +16,8 @@ MeshSurfaceFilter::from_xml(pugi::xml_node node)
 }
 
 void
-MeshSurfaceFilter::get_all_bins(Particle* p, int estimator, FilterMatch& match)
-const
+MeshSurfaceFilter::get_all_bins(const Particle* p, int estimator,
+                                FilterMatch& match) const
 {
   meshes[mesh_]->surface_bins_crossed(p, match.bins_);
   for (auto b : match.bins_) match.weights_.push_back(1.0);
@@ -37,30 +37,43 @@ MeshSurfaceFilter::text_label(int bin) const
   std::string out = MeshFilter::text_label(i_mesh);
 
   // Get surface part of label.
-  if (i_surf == OUT_LEFT) {
-    out += " Outgoing, x-min";
-  } else if (i_surf == IN_LEFT) {
-    out += " Incoming, x-min";
-  } else if (i_surf == OUT_RIGHT) {
-    out += " Outgoing, x-max";
-  } else if (i_surf == IN_RIGHT) {
-    out += " Incoming, x-max";
-  } else if (i_surf == OUT_BACK) {
-    out += " Outgoing, y-min";
-  } else if (i_surf == IN_BACK) {
-    out += " Incoming, y-min";
-  } else if (i_surf == OUT_FRONT) {
-    out += " Outgoing, y-max";
-  } else if (i_surf == IN_FRONT) {
-    out += " Incoming, y-max";
-  } else if (i_surf == OUT_BOTTOM) {
-    out += " Outgoing, z-min";
-  } else if (i_surf == IN_BOTTOM) {
-    out += " Incoming, z-min";
-  } else if (i_surf == OUT_TOP) {
-    out += " Outgoing, z-max";
-  } else if (i_surf == IN_TOP) {
-    out += " Incoming, z-max";
+  switch (i_surf) {
+    case OUT_LEFT:
+      out += " Outgoing, x-min";
+      break;
+    case IN_LEFT:
+      out += " Incoming, x-min";
+      break;
+    case OUT_RIGHT:
+      out += " Outgoing, x-max";
+      break;
+    case IN_RIGHT:
+      out += " Incoming, x-max";
+      break;
+    case OUT_BACK:
+      out += " Outgoing, y-min";
+      break;
+    case IN_BACK:
+      out += " Incoming, y-min";
+      break;
+    case OUT_FRONT:
+      out += " Outgoing, y-max";
+      break;
+    case IN_FRONT:
+      out += " Incoming, y-max";
+      break;
+    case OUT_BOTTOM:
+      out += " Outgoing, z-min";
+      break;
+    case IN_BOTTOM:
+      out += " Incoming, z-min";
+      break;
+    case OUT_TOP:
+      out += " Outgoing, z-max";
+      break;
+    case IN_TOP:
+      out += " Incoming, z-max";
+      break;
   }
 
   return out;
diff --git a/src/tallies/filter_mu.cpp b/src/tallies/filter_mu.cpp
index cd428a4e41..e57a8aa2e5 100644
--- a/src/tallies/filter_mu.cpp
+++ b/src/tallies/filter_mu.cpp
@@ -4,6 +4,7 @@
 
 #include "openmc/error.h"
 #include "openmc/search.h"
+#include "openmc/xml_interface.h"
 
 namespace openmc {
 
@@ -34,12 +35,14 @@ MuFilter::from_xml(pugi::xml_node node)
 }
 
 void
-MuFilter::get_all_bins(Particle* p, int estimator, FilterMatch& match) const
+MuFilter::get_all_bins(const Particle* p, int estimator, FilterMatch& match)
+const
 {
-  if (p->mu >= bins_[0] && p->mu <= bins_.back()) {
+  if (p->mu >= bins_.front() && p->mu <= bins_.back()) {
+    //TODO: off-by-one
     auto bin = lower_bound_index(bins_.begin(), bins_.end(), p->mu) + 1;
     match.bins_.push_back(bin);
-    match.weights_.push_back(1);
+    match.weights_.push_back(1.0);
   }
 }
 
diff --git a/src/tallies/filter_polar.cpp b/src/tallies/filter_polar.cpp
index 81839cecb4..bfa87a3417 100644
--- a/src/tallies/filter_polar.cpp
+++ b/src/tallies/filter_polar.cpp
@@ -5,6 +5,7 @@
 #include "openmc/constants.h"
 #include "openmc/error.h"
 #include "openmc/search.h"
+#include "openmc/xml_interface.h"
 
 namespace openmc {
 
@@ -35,7 +36,7 @@ PolarFilter::from_xml(pugi::xml_node node)
 }
 
 void
-PolarFilter::get_all_bins(Particle* p, int estimator, FilterMatch& match)
+PolarFilter::get_all_bins(const Particle* p, int estimator, FilterMatch& match)
 const
 {
   double theta;
@@ -45,10 +46,11 @@ const
     theta = std::acos(p->last_uvw[2]);
   }
 
-  if (theta >= bins_[0] && theta <= bins_.back()) {
+  if (theta >= bins_.front() && theta <= bins_.back()) {
+    //TODO: off-by-one
     auto bin = lower_bound_index(bins_.begin(), bins_.end(), theta) + 1;
     match.bins_.push_back(bin);
-    match.weights_.push_back(1);
+    match.weights_.push_back(1.0);
   }
 }
 
diff --git a/src/tallies/filter_sph_harm.cpp b/src/tallies/filter_sph_harm.cpp
index f6d1656216..1c085bcce1 100644
--- a/src/tallies/filter_sph_harm.cpp
+++ b/src/tallies/filter_sph_harm.cpp
@@ -3,6 +3,7 @@
 #include "openmc/capi.h"
 #include "openmc/error.h"
 #include "openmc/math_functions.h"
+#include "openmc/xml_interface.h"
 
 namespace openmc {
 
@@ -28,7 +29,7 @@ SphericalHarmonicsFilter::from_xml(pugi::xml_node node)
 }
 
 void
-SphericalHarmonicsFilter::get_all_bins(Particle* p, int estimator,
+SphericalHarmonicsFilter::get_all_bins(const Particle* p, int estimator,
                                        FilterMatch& match) const
 {
   // Determine cosine term for scatter expansion if necessary
@@ -51,6 +52,7 @@ SphericalHarmonicsFilter::get_all_bins(Particle* p, int estimator,
     // Append the matching (bin,weight) for each moment
     for (int i = 0; i < num_nm; i++) {
       match.weights_.push_back(wgt[n] * rn[j]);
+      //TODO: off-by-one
       match.bins_.push_back(++j);
     }
   }
diff --git a/src/tallies/filter_sptl_legendre.cpp b/src/tallies/filter_sptl_legendre.cpp
index a5507b614b..4043a43895 100644
--- a/src/tallies/filter_sptl_legendre.cpp
+++ b/src/tallies/filter_sptl_legendre.cpp
@@ -3,6 +3,7 @@
 #include "openmc/capi.h"
 #include "openmc/error.h"
 #include "openmc/math_functions.h"
+#include "openmc/xml_interface.h"
 
 namespace openmc {
 
@@ -29,8 +30,8 @@ SpatialLegendreFilter::from_xml(pugi::xml_node node)
 }
 
 void
-SpatialLegendreFilter::get_all_bins(Particle* p, int estimator, FilterMatch& match)
-const
+SpatialLegendreFilter::get_all_bins(const Particle* p, int estimator,
+                                    FilterMatch& match) const
 {
   // Get the coordinate along the axis of interest.
   double x;
@@ -50,6 +51,7 @@ const
     double wgt[order_ + 1];
     calc_pn_c(order_, x_norm, wgt);
     for (int i = 0; i < order_ + 1; i++) {
+      //TODO: off-by-one
       match.bins_.push_back(i + 1);
       match.weights_.push_back(wgt[i]);
     }
diff --git a/src/tallies/filter_surface.cpp b/src/tallies/filter_surface.cpp
index 9ce61e84db..7fd2c6e24e 100644
--- a/src/tallies/filter_surface.cpp
+++ b/src/tallies/filter_surface.cpp
@@ -4,6 +4,7 @@
 
 #include "openmc/error.h"
 #include "openmc/surface.h"
+#include "openmc/xml_interface.h"
 
 namespace openmc {
 
@@ -17,6 +18,7 @@ SurfaceFilter::from_xml(pugi::xml_node node)
 void
 SurfaceFilter::initialize()
 {
+  // Convert surface IDs to indices of the global array.
   for (auto& s : surfaces_) {
     auto search = surface_map.find(s);
     if (search != surface_map.end()) {
@@ -29,22 +31,24 @@ SurfaceFilter::initialize()
     }
   }
 
+  // Populate the index->bin map.
   for (int i = 0; i < surfaces_.size(); i++) {
     map_[surfaces_[i]] = i;
   }
 }
 
 void
-SurfaceFilter::get_all_bins(Particle* p, int estimator, FilterMatch& match)
-const
+SurfaceFilter::get_all_bins(const Particle* p, int estimator,
+                            FilterMatch& match) const
 {
   auto search = map_.find(std::abs(p->surface)-1);
   if (search != map_.end()) {
+    //TODO: off-by-one
     match.bins_.push_back(search->second + 1);
     if (p->surface < 0) {
-      match.weights_.push_back(-1);
+      match.weights_.push_back(-1.0);
     } else {
-      match.weights_.push_back(1);
+      match.weights_.push_back(1.0);
     }
   }
 }
diff --git a/src/tallies/filter_universe.cpp b/src/tallies/filter_universe.cpp
index bd90ed091b..de0d33d294 100644
--- a/src/tallies/filter_universe.cpp
+++ b/src/tallies/filter_universe.cpp
@@ -4,6 +4,7 @@
 
 #include "openmc/cell.h"
 #include "openmc/error.h"
+#include "openmc/xml_interface.h"
 
 namespace openmc {
 
@@ -17,6 +18,7 @@ UniverseFilter::from_xml(pugi::xml_node node)
 void
 UniverseFilter::initialize()
 {
+  // Convert universe IDs to indices of the global array.
   for (auto& u : universes_) {
     auto search = universe_map.find(u);
     if (search != universe_map.end()) {
@@ -29,20 +31,22 @@ UniverseFilter::initialize()
     }
   }
 
+  // Populate the index->bin map.
   for (int i = 0; i < universes_.size(); i++) {
     map_[universes_[i]] = i;
   }
 }
 
 void
-UniverseFilter::get_all_bins(Particle* p, int estimator, FilterMatch& match)
-const
+UniverseFilter::get_all_bins(const Particle* p, int estimator,
+                             FilterMatch& match) const
 {
   for (int i = 0; i < p->n_coord; i++) {
     auto search = map_.find(p->coord[i].universe);
     if (search != map_.end()) {
+      //TODO: off-by-one
       match.bins_.push_back(search->second + 1);
-      match.weights_.push_back(1);
+      match.weights_.push_back(1.0);
     }
   }
 }
diff --git a/src/tallies/filter_zernike.cpp b/src/tallies/filter_zernike.cpp
index c7413f3416..ed658e2d28 100644
--- a/src/tallies/filter_zernike.cpp
+++ b/src/tallies/filter_zernike.cpp
@@ -6,6 +6,7 @@
 #include "openmc/capi.h"
 #include "openmc/error.h"
 #include "openmc/math_functions.h"
+#include "openmc/xml_interface.h"
 
 namespace openmc {
 
@@ -16,16 +17,15 @@ namespace openmc {
 void
 ZernikeFilter::from_xml(pugi::xml_node node)
 {
-  order_ = std::stoi(get_node_value(node, "order"));
+  set_order(std::stoi(get_node_value(node, "order")));
   x_ = std::stod(get_node_value(node, "x"));
   y_ = std::stod(get_node_value(node, "y"));
   r_ = std::stod(get_node_value(node, "r"));
-  calc_n_bins();
 }
 
 void
-ZernikeFilter::get_all_bins(Particle* p, int estimator, FilterMatch& match)
-const
+ZernikeFilter::get_all_bins(const Particle* p, int estimator,
+                            FilterMatch& match) const
 {
   // Determine the normalized (r,theta) coordinates.
   double x = p->coord[0].xyz[0] - x_;
@@ -38,6 +38,7 @@ const
     double zn[n_bins_];
     calc_zn(order_, r, theta, zn);
     for (int i = 0; i < n_bins_; i++) {
+      //TODO: off-by-one
       match.bins_.push_back(i+1);
       match.weights_.push_back(zn[i]);
     }
@@ -69,12 +70,19 @@ ZernikeFilter::text_label(int bin) const
   }
 }
 
+void
+ZernikeFilter::set_order(int order)
+{
+  order_ = order;
+  n_bins_ = ((order+1) * (order+2)) / 2;
+}
+
 //==============================================================================
 // ZernikeRadialFilter implementation
 //==============================================================================
 
 void
-ZernikeRadialFilter::get_all_bins(Particle* p, int estimator,
+ZernikeRadialFilter::get_all_bins(const Particle* p, int estimator,
                                   FilterMatch& match) const
 {
   // Determine the normalized radius coordinate.
@@ -87,6 +95,7 @@ ZernikeRadialFilter::get_all_bins(Particle* p, int estimator,
     double zn[n_bins_];
     calc_zn_rad(order_, r, zn);
     for (int i = 0; i < n_bins_; i++) {
+      //TODO: off-by-one
       match.bins_.push_back(i+1);
       match.weights_.push_back(zn[i]);
     }
@@ -99,6 +108,13 @@ ZernikeRadialFilter::text_label(int bin) const
   return "Zernike expansion, Z" + std::to_string(2*(bin-1)) + ",0";
 }
 
+void
+ZernikeRadialFilter::set_order(int order)
+{
+  order_ = order;
+  n_bins_ = order / 2 + 1;
+}
+
 //==============================================================================
 // C-API functions
 //==============================================================================
@@ -116,7 +132,7 @@ openmc_zernike_filter_get_order(int32_t index, int* order)
   }
 
   auto z_filt = static_cast<ZernikeFilter*>(filt);
-  *order = z_filt->order_;
+  *order = z_filt->order();
   return 0;
 }
 
@@ -153,8 +169,7 @@ openmc_zernike_filter_set_order(int32_t index, int order)
   }
 
   auto z_filt = static_cast<ZernikeFilter*>(filt);
-  z_filt->order_ = order;
-  z_filt->calc_n_bins();
+  z_filt->set_order(order);
   filter_update_n_bins(index);
   return 0;
 }