diff --git a/CMake/itkExternal_FFTW.cmake b/CMake/itkExternal_FFTW.cmake
index 6d9e6918350..7c70f641c57 100644
--- a/CMake/itkExternal_FFTW.cmake
+++ b/CMake/itkExternal_FFTW.cmake
@@ -1,19 +1,38 @@
 #
 # Encapsulates building FFTW as an External Project.
 #
-# NOTE: internal building of fftw is for convenience,
-#       and the version of fftw built here does not
-#       use modern hardware optimzations.
+# SIMD codelet selection
+# ----------------------
+# FFTW SIMD codelets are hand-written assembly routines baked into the
+# library at compile time.  Passing -march=native to the ITK build does
+# NOT activate them; they must be requested explicitly via FFTW's own
+# CMake options (ENABLE_NEON, ENABLE_SSE, ENABLE_SSE2, ENABLE_AVX, ENABLE_AVX2).
 #
-#       The build configuration chosen to be
-#       generalizable to as many hardware platforms.
-#       Being backward compatible for decades
-#       old hardware is the goal of this internal
-#       representation.
+# This file detects appropriate defaults at cmake configure time:
 #
-#       This is primarily used to support testing
-#       and should not be used for production
-#       builds where performance is a concern.
+#   Native builds (CMAKE_CROSSCOMPILING is false):
+#     - ARM64 (aarch64/arm64/ARM64): NEON=ON (mandatory in ARMv8); x86 SIMD off.
+#     - x86/x86_64 with GCC/Clang: each of SSE, SSE2, AVX, AVX2 is probed
+#       individually via __builtin_cpu_supports() / CheckCSourceRuns so that
+#       the detected flags match the actual build-host CPU.  A pre-AVX
+#       Sandy Bridge gets SSE+SSE2 only; a Haswell or later gets all four.
+#       On MSVC the probes are skipped (intrinsic unavailable) and SIMD
+#       defaults to off; users can override via FFTW_ENABLE_* options.
+#     - Other architectures: all SIMD off (conservative fallback).
+#
+#   Cross-compiled builds (CMAKE_CROSSCOMPILING is true):
+#     - ARM64: NEON=ON (mandatory); x86 SIMD off.
+#     - x86_64: SSE+SSE2 only (baseline; AVX/AVX2 not assumed for target).
+#     - Other: all SIMD off.
+#
+# Every flag is an individually overridable cache option, e.g.:
+#   cmake -DFFTW_ENABLE_AVX2=OFF ...
+# Note: option() defaults are only applied on the first configure.
+# To re-detect after a toolchain change, delete the CMake cache or use
+# cmake --fresh, or pass explicit -DFFTW_ENABLE_*= overrides.
+#
+# ENABLE_SSE (SSE1) is float-only and is not forwarded to the
+# double-precision fftwd build.
 #
 # These instructions follow the guidance provided for modern cmake usage as described:
 # https://github.com/dev-cafe/cmake-cookbook/blob/master/chapter-08/recipe-03/c-example/external/upstream/fftw3/CMakeLists.txt
@@ -64,6 +83,79 @@ if(NOT ITK_USE_SYSTEM_FFTW)
 
   set(FFTW_STAGED_INSTALL_PREFIX "${ITK_BINARY_DIR}/fftw")
 
+  # Detect SIMD defaults (see file header for full policy description).
+  # CheckCSourceRuns results are cached after the first cmake configure run.
+  include(CheckCSourceRuns)
+
+  set(_fftw_default_neon OFF)
+  set(_fftw_default_sse OFF)
+  set(_fftw_default_sse2 OFF)
+  set(_fftw_default_avx OFF)
+  set(_fftw_default_avx2 OFF)
+
+  if(NOT CMAKE_CROSSCOMPILING)
+    if(CMAKE_SYSTEM_PROCESSOR MATCHES "aarch64|arm64|ARM64")
+      # NEON is mandatory in ARMv8/AArch64 — every arm64 CPU has it.
+      set(_fftw_default_neon ON)
+    elseif(CMAKE_SYSTEM_PROCESSOR MATCHES "x86_64|AMD64|i686")
+      # Probe each x86 SIMD level individually via CPUID so the defaults
+      # are accurate for the actual build-host CPU (e.g. pre-AVX Sandy Bridge
+      # or pre-AVX2 Ivy Bridge get only the levels their hardware supports).
+      # __builtin_cpu_supports is a GCC/Clang intrinsic; skip on MSVC.
+      if(CMAKE_C_COMPILER_ID MATCHES "GNU|Clang|AppleClang")
+        foreach(_fftw_simd IN ITEMS sse sse2 avx avx2)
+          check_c_source_runs(
+            "int main(void){return __builtin_cpu_supports(\"${_fftw_simd}\")?0:1;}"
+            _fftw_cpu_has_${_fftw_simd}
+          )
+          if(_fftw_cpu_has_${_fftw_simd})
+            set(_fftw_default_${_fftw_simd} ON)
+          endif()
+        endforeach()
+      endif()
+    endif()
+  else()
+    # Cross-compiling: conservative architecture-level fallback.
+    if(CMAKE_SYSTEM_PROCESSOR MATCHES "aarch64|arm64|ARM64")
+      set(_fftw_default_neon ON)
+    elseif(CMAKE_SYSTEM_PROCESSOR MATCHES "x86_64|AMD64")
+      # SSE/SSE2 are baseline on all 64-bit x86 CPUs; AVX/AVX2 not assumed.
+      set(_fftw_default_sse ON)
+      set(_fftw_default_sse2 ON)
+    endif()
+  endif()
+
+  option(
+    FFTW_ENABLE_NEON
+    "Enable FFTW NEON SIMD codelets (ARM64)"
+    ${_fftw_default_neon}
+  )
+  option(
+    FFTW_ENABLE_SSE
+    "Enable FFTW SSE SIMD codelets (x86)"
+    ${_fftw_default_sse}
+  )
+  option(
+    FFTW_ENABLE_SSE2
+    "Enable FFTW SSE2 SIMD codelets (x86)"
+    ${_fftw_default_sse2}
+  )
+  option(
+    FFTW_ENABLE_AVX
+    "Enable FFTW AVX SIMD codelets (x86)"
+    ${_fftw_default_avx}
+  )
+  option(
+    FFTW_ENABLE_AVX2
+    "Enable FFTW AVX2 SIMD codelets (x86)"
+    ${_fftw_default_avx2}
+  )
+
+  message(
+    STATUS
+    "FFTW SIMD: NEON=${FFTW_ENABLE_NEON} SSE=${FFTW_ENABLE_SSE} SSE2=${FFTW_ENABLE_SSE2} AVX=${FFTW_ENABLE_AVX} AVX2=${FFTW_ENABLE_AVX2}"
+  )
+
   # Macro to generate library filename with appropriate prefix/suffix
   # Args: output_var library_base_name
   macro(_library_name_to_filename output_var library_base_name)
@@ -111,10 +203,12 @@ if(NOT ITK_USE_SYSTEM_FFTW)
         -DCMAKE_INSTALL_PREFIX:PATH=${FFTW_STAGED_INSTALL_PREFIX}
         -DCMAKE_INSTALL_LIBDIR:STRING=${CMAKE_INSTALL_LIBDIR}
         -DCMAKE_INSTALL_BINDIR:STRING=${CMAKE_INSTALL_BINDIR}
-        -DDISABLE_FORTRAN:BOOL=ON -DENABLE_AVX:BOOL=OFF -DENABLE_AVX2:BOOL=OFF
-        -DENABLE_FLOAT:BOOL=ON -DENABLE_LONG_DOUBLE:BOOL=OFF
+        -DDISABLE_FORTRAN:BOOL=ON -DENABLE_AVX:BOOL=${FFTW_ENABLE_AVX}
+        -DENABLE_AVX2:BOOL=${FFTW_ENABLE_AVX2} -DENABLE_FLOAT:BOOL=ON
+        -DENABLE_LONG_DOUBLE:BOOL=OFF -DENABLE_NEON:BOOL=${FFTW_ENABLE_NEON}
         -DENABLE_OPENMP:BOOL=OFF -DENABLE_QUAD_PRECISION:BOOL=OFF
-        -DENABLE_SSE:BOOL=OFF -DENABLE_SSE2:BOOL=OFF -DENABLE_THREADS:BOOL=ON
+        -DENABLE_SSE:BOOL=${FFTW_ENABLE_SSE}
+        -DENABLE_SSE2:BOOL=${FFTW_ENABLE_SSE2} -DENABLE_THREADS:BOOL=ON
         -DCMAKE_APPLE_SILICON_PROCESSOR:STRING=${CMAKE_APPLE_SILICON_PROCESSOR}
         -DCMAKE_C_COMPILER_LAUNCHER:PATH=${CMAKE_C_COMPILER_LAUNCHER}
         -DCMAKE_C_COMPILER:PATH=${CMAKE_C_COMPILER}
@@ -175,10 +269,12 @@ if(NOT ITK_USE_SYSTEM_FFTW)
         -DCMAKE_INSTALL_PREFIX:PATH=${FFTW_STAGED_INSTALL_PREFIX}
         -DCMAKE_INSTALL_LIBDIR:STRING=${CMAKE_INSTALL_LIBDIR}
         -DCMAKE_INSTALL_BINDIR:STRING=${CMAKE_INSTALL_BINDIR}
-        -DDISABLE_FORTRAN:BOOL=ON -DENABLE_AVX:BOOL=OFF -DENABLE_AVX2:BOOL=OFF
-        -DENABLE_FLOAT:BOOL=OFF -DENABLE_LONG_DOUBLE:BOOL=OFF
+        -DDISABLE_FORTRAN:BOOL=ON -DENABLE_AVX:BOOL=${FFTW_ENABLE_AVX}
+        -DENABLE_AVX2:BOOL=${FFTW_ENABLE_AVX2} -DENABLE_FLOAT:BOOL=OFF
+        -DENABLE_LONG_DOUBLE:BOOL=OFF -DENABLE_NEON:BOOL=${FFTW_ENABLE_NEON}
         -DENABLE_OPENMP:BOOL=OFF -DENABLE_QUAD_PRECISION:BOOL=OFF
-        -DENABLE_SSE:BOOL=OFF -DENABLE_SSE2:BOOL=OFF -DENABLE_THREADS:BOOL=ON
+        -DENABLE_SSE:BOOL=OFF # SSE1 codelets are 32-bit float only; no effect on double-precision
+        -DENABLE_SSE2:BOOL=${FFTW_ENABLE_SSE2} -DENABLE_THREADS:BOOL=ON
         -DCMAKE_APPLE_SILICON_PROCESSOR:STRING=${CMAKE_APPLE_SILICON_PROCESSOR}
         -DCMAKE_C_COMPILER_LAUNCHER:PATH=${CMAKE_C_COMPILER_LAUNCHER}
         -DCMAKE_C_COMPILER:PATH=${CMAKE_C_COMPILER}