Smooth Mouse-Look

I've created a fairly simple mouse-look script for an fps game i'm working on, however I've noticed that while the mouse movement appears smooth, whenever I strafe around objects I get this annoying jittery look on objects that I focus on. Can someone take a look at my code, and tell me how I might improve it?

Code (CSharp):

1. public class PlayerLook : MonoBehaviour
2. {
3.     public float mouseSensitivity = 100.0f;
4.     public float clampAngle = 80.0f;
5.  
6.     private float mouseX;
7.     private float mouseY;
8.  
9.     private float rotationX = 0.0f;
10.     private float rotationY = 0.0f;
11.  
12.     void Start()
13.     {
14.         Vector3 rotation = transform.localRotation.eulerAngles;
15.         rotationX = rotation.x;
16.         rotationY = rotation.y;
17.     }
18.  
19.     void Update()
20.     {
21.         mouseX = Input.GetAxis("Mouse X");
22.         mouseY = Input.GetAxis("Mouse Y");
23.  
24.         rotationX += mouseY * mouseSensitivity * Time.deltaTime;
25.         rotationY += mouseX * mouseSensitivity * Time.deltaTime;  
26.  
27.         rotationX = Mathf.Clamp(rotationX, -clampAngle, clampAngle);
28.  
29.         Quaternion localRotation = Quaternion.Euler(rotationX, rotationY, 0.0f);
30.  
31.         transform.rotation = Quaternion.Lerp(transform.rotation, localRotation, Time.fixedTime);
32.     }
33. }

 

I think I figured it out, my update functions on my rigidbody player and my mouse-look camera were different from each other. I changed them both to FixedUpdate and now it looks much smoother.