How to make a camera-window in Unity3D

Question

I am programing a 2.5 D Spaceshooter game. Unfortunately, I have some problems with the camera.

With this code, my Camera follows only the spaceship.

using UnityEngine;
using System.Collections;

public class CameraController : MonoBehaviour {

public GameObject player;

  private Vector3 offset;

  void Start ()
  {
      offset = transform.position - player.transform.position;
  }

  void LateUpdate ()
  {
      transform.position = player.transform.position + offset;
  }
}

The camera should slightly follow the spaceship but should not go out of the boundary like this video: https://www.youtube.com/watch?v=2DN3p8aYOKg

Update: Thanks for the answers. Maybe I should specify my question a little bit. On the website: http://gamasutra.com/blogs/ItayKeren/20150511/243083/Scroll_Back_The_Theory_and_Practice_of_Cameras_in_SideScrollers.php#h.elfjc4ap4hpe There is a example with Curb Camera Motion. I want to make a camera-window which pushes the camera position as the player hits the window edge.

Any ideas, how to realize this?